Yes. And as you have supposed, simply ejecting "sperm" into a common pool (or more technically, motile isogametes) is the most straightforward way to do it. How do you prevent single-parent offspring? The same way that many real-world isogamous species do: by instituting mating types. I.e., you may have 7, 11, 29, or even larger (not necessarily prime) numbers of distinct biological sexes distinguished by nothing more than the chemical markers on their gametes that prevent them from fertilizing themselves, and with no more sociological significance than blood types.

How do you prevent it from resulting in millions of offspring at a time? Well, that's easy--you just decide to be careful about what counts as "offspring". If you count individual embryos, that might be tough--but externally fertilized individual embryos don't have a fantastic survival rate if they aren't intentionally cared for, and that's hard to do when they're microscopic! So, just establish a convention that offspring don't count until they reach a certain minimum developmental stage--anything that dies earlier is just a "failed pregnancy". Then you just need to figure out how to kill off most of them--which, again, isn't hard. If you want to make sure that there is a natural tendency for any particular intentional procreative event to average one surviving offspring, just make the larva cannibalistic--only one or two will manage to make it past "fetus" stage after having eaten all of their brothers.

For a more complicated option, consider hybridization with sexual parasitism--in which case you really can have "males" of one species, as distinguished from the males and females of a different species. The simplest way to work this is to have the all-male species' sperm hijack the eggs of their host species' females, ejecting the host's DNA and resulting in the incubation and birth of a new male every time, with no (or at least minimal--perhaps they preserve the equivalent of mitochondrial DNA from the host mother) gene transfer between species. While mechanically that looks like sexual reproduction, however, genetically speaking it is effectively asexual, with all males being nuclear clones of each other. There are a couple of ways around this.

1. Maternal DNA is not discarded during fertilization, but during
   meiosis. I.e., every male is actually a hybrid, carrying the unique
   DNA of his own species from his father, and half of the DNA from his
   extra-specific mother. When he manufactures sperm, however, the
   maternal DNA is preferentially discarded, ensuring that the paternal
   DNA is propagated unchanged between generations, and merely
   re-hybridized with new host females each time. This ensure no
   permanent gene flow between the populations of the all-male
   parasites and their female-having host species, and limits evolution
   of the parasite male chromosomes to spontaneous mutation like an
   asexual species, but still allows the parasite male population to
   effectively evolve alongside, and benefit from the evolution of,
   their host population.



2. 
   

   If we want gene transfer between males, you will need to
   introduce an additional step--a host species which is internally
   fertile with both males and females, a hybrid form which may or may
   not be internally fertile, and the parasitic all-male species. This
   can go a few different ways, depending on the fertility
   characteristics of the hybrid form(s), but the next simplest option
   in this case is to make male hybrids either completely sterile or
   simply non-existent (i.e., any hybrid male embryos are simply
   non-viable, like a human YY embryo would be), leaving only female
   hybrids able to procreate with at least the all-male parasite species,
   and optionally with the the host disexual species.
   In either case, we assume that there
   is some unique genetic material (i.e., mis-matched chromosomes) that
   can be distinguished between species and does not transfer between
   them, although there may be some mixing in other parts of the
   genome--this shouldn't be too big of a deal, since the two species
   involved would have to have started out pretty closely related
   anyway in order for hybridization to be possible, so they'll only be
   sharing genes that they already had in common anyway. Parasite
   male-species reproduction then occurs in two steps:

   
   
   

   a) a parasite male mates with a host female to produce a hybrid female

   
   
   

   b) a parasite male mates with a hybrid female, resulting in a parasite male who is the nearly-pure genetic child of his father and maternal grandfather.

   
   
   

   Of course, we have to explain why hybrid females can't produce more hybrid females as offspring when mating with parasite males; if they could, we'd be left to wonder why this does not result in simply discarding the host species and adopting the hybrids as the new females of the formerly-parasitic species. Once again, we can go in many directions with this, but we'll pick the simplest--as in option 1, hybrid meiosis discards the identifiably-maternal genome, so hybrids can in fact only produce parasite male offspring, not new hybrid females after all. This results in fully-recombinant sexual reproduction between members of the all-male species, spread out over an intermediate generation; and while unlike option 1 it does permit some gene flow between parasite and host species, that can be limited to only a fraction of the chromosome complement of each species, which would have to remain similar anyway for hybridization to remain viable, and does not impact the purity of the distinctive male genetic line or allow the distinctive genes of the parasite species to flow into the host species population.

   
   

For a (somewhat more complicated) real-life example of this kind of all-male species that reproduces through hybridization consider a certain clade of Australian fish in a four-way species complex. Now, not 100% of them are male, but it's pretty dang close.

Now, why is this two-or-three-part species complex not just considered one species with a bunch of different gender morphs, regardless of their ancestry from two originally separate species? Aside from the genetic arguments (which would not necessarily be readily available to them or to humans at first glance), it is not difficult to come up with cultural ones. A fairly straightforward explanation, for example, could be that the host species is just not that smart--equivalent to, say, bonobos, while the parasite species is on-par with modern humans. This is analogous to the situation with Larry Niven's Pierson's Puppeteers--their sexual host species (with whom they have zero genetic transfer, as it requires two Puppeteers to inseminate a host female, completely ignoring the female's contribution) is essentially livestock. If they don't want to consider their sexual hosts to be of the same species as them, and the hosts can't exactly protest that categorization, humans are likely to along with it.

Oglaf, a totally NSFW comic which I won't link to, has an all male tribe. It's mostly a joke though, with men impregnating men and babies magically coming out of their assets.

For a purely male species with the requirements you provided, you could have it like this:

• Individuals reproduce by binary fission;


• If an individual has received sperm from another individual, the receiver can mix their own original genes with those they received; and not in a small group of special cells, but throughout their whole body.

Some bacteria like our symbiont E. coli do something similar, it's called conjugation and goes like this:

It wouldn't be a stretch to adapt this to multicellular life in a work of fiction.

Virii also seem to match what you want. The absolute vast majority of them only ever impregnates other life with their DNA; only a small minority may be impregnated, and always by virii of other species. Now, granted, they are acellular; but that, again, can be adapted to multicellular life.

Last thing I can think of are hybrids of any two species, for which only the male hybrids are viable. They don't belong to either of their parents' species, and the whole population will be male. What allows them to reproduce is mating with a female of either parents' species; the amount of viable offspring may be small, producing one might be like winning the lottery. This would keep their numbers really low. Add that for some reason the male cares for the egg, which is not unusual in nature, and there you have it.

The eggs are ancient.

In this scenario, the males fertilize eggs in the manner of fish or amphibians, spraying milt on one or more eggs and so triggering their development.

The eggs in question come from a huge secret cache, a shrine of sorts to this species. In this cave are hundreds of thousands of unfertilized eggs, left there by the long vanished females. The males tend these unfertilized eggs and keep them viable. When reproduction is in order a male will take one out, fertilize it and tend it much in the way a male fish like a bass or a tilapia will tend his nest of fertilized eggs.

There will never be any more eggs. When they run out the species goes extinct. But that will not be for a long time - there are a lot of eggs in this cave.

Haldane's Rule says unlikely (but doesn't always hold, even on Earth.)

Back in 1922, a smart guy named Haldane formulated a rule: if, in a species hybrid, only one sex is inviable or sterile, that sex is more likely to be the heterogametic sex. (The heterogametic sex is the one with two different sex chromosomes; in therian mammals, for example, this is the male.)

Or you could read up on an all-female fish species if that also interests you.

Extreme sexual dimorphism

You can have a "female" organism that has evolved into a sessile, predatory form, and a "male" organism that is motile.

The female produces ova, and also secretes pheromones that attract mature males (as well as other prey). Similar to the praying mantis, if the female is well fed enough it won't kill the male. With the development of male sentience, this is pretty easy to accomplish. Older and weaker males get absorbed, similar to what happens to anglerfish.

Being a top predator and having no natural enemies, the female organism never developed intelligence and is optimized for reproduction. Very young females are motile, and can wander far enough from the mother to establish a new lair. Males, on the other hand, can go wherever they want.

While flatworms are technically considered hermaphroditic, they may stand as a close existing example to what you have in mind. Flatworms have penises without vaginas; so, from the outside they appear to be an all male species. The way they reproduce is to basically stab each other with their male organs, and the sperm has to find its way to the eggs https://en.wikipedia.org/wiki/Penis_fencing.

If you want to take it a step further into fiction such that there are not even internal female organs, female like systems could be made ad hoc via stem cells as a natural reaction to being stabbed and inseminated. Imaging a scenario where stem cells from the creature's bone marrow goes through the blood to the injury the same way we do when our bodies try to heal after being stabbed, but the semon causes a biological reaction where by the first stem cell forms into an egg, and then the following stem cells respond by surrounding the egg in a uterus like cyst. Once the fetus matures enough, the cyst ruptures or the baby eats its way out.

Since Female tends to imply bearing young, no unless the males impregnate some other host that will then bear young. In this case the race of all males is more like a race of parasites.

The trick here is that the second race must be able to mate viably with itself (has males and females and can make babies). That keeps that other race as a separate race whose biological systems are hijacked by the parasitical race.

Some fishes have rudimentary males. Rudimentary females are not known, but can be imagined. If males are something as sea horses, with eggs growing in the pocket on the male's body with females very small and living also on the males, in the same pocket, only forever.

Moties?

Larry Niven's moties sprang to mind.

They change sex.

They had a problem, in that the only way to get from female back to male was to have a baby. But perhaps the answer for this question is that they cycle between male and female for their entire life, without problems, being male 95%+ of the time. I'm imagining them as somewhat like marsupials, with a permanent pouch. Or maybe they lay eggs, like birds. The change from biological male to biological female is quite slight in physical terms. It's like a terrestrial mammalian female coming into heat. The male organ becomes inhibited, and an egg becomes available for fertilisation. If it is fertilized, soon afterwards a tiny almost-embryonic baby crawls into the pouch. Its parent shortly afterwards reverts to being "male", whether or not s/he has a baby in ver pouch.

Not hermaphrodite, because only one sexual role is expressible at once. Not a big thing, either. All of these creatures have the same ability to bear babies in a pouch all their lives -- it is not seen as anything special. Ditto child-rearing. "Female" is just a transient phase everybody goes though for a few days maybe once a year.

(On the evolutionary front, rape probably has to be impossible, with so many males and so few females. Sexual arrangements like many birds? Non-penetrative, and futile without cooperation by the "female". Possibly also "promiscuous" like domestic cats, and some birds)

For a species like Bortas, it could be that sexual functions are not coded in exactly one pair of chromosomes, like most sexual species on earth. It would seem that Bortas and his mate, Klyden, are both functionally capable of reproduction, by way of laying an egg and fertilizing said egg. Remember, if they were traditionally sexed, Bortas is Topha's mother (he lays the egg) and Klyden is the father, but we learn Klyden was born Female while Bortas is definitely male by birth. The rate of female births is once every 70 years, but we see three Moclan born-women in the episode, which doesn't track.

My theory is that Mochlins have three or more independent sexual codings: One coding would produce female genetalia and the ability to produce female gametes (Eggs) while another coding would produce the male gametes (sperm) and a third would produce male genitalia. This could produce a species that could functionally be hermaphroditic but visually be sexually dimorphic. While the female aspects of reproduction and the production of male gametes are always functional, it could be that the male genetalia exists on an XY type chromosome where a YY or XY pairing will produce the genetalia but an XX will not.

This would preserve the single sex nature of the Moclans as "males" and "females" are both capable of producing a healthy off spring, but men could reproduce with men or women where as women could only reproduce with men. It's conceivable that somewhere in the evolution of the modern Moclan, it was reasoned that having a mate who was both capable of laying eggs and fertilizing your eggs was more desirable than having a mate that could not fertilize your eggs.

This fits with Moclans rather subtle but still present dislike of women and their tendency to be quite hostile in their social mechanisms. Their favorite sport is a game of hot potato where the ball will eventually stab you through the hand... at which point you win. Their divorce proceedings are basically stab your partner in the chest... if he dies, you are divorced... the one woman who remained as such hid in caves to conceal her identity and in the instance of a male Moclin who fancied women over men, Klyden, who long seems to be the cultural norm of typical Moclin society, is ready to ruin the straight Moclin's life and seeths with hatred equal to the most extremen homophobe on earth. It could be, that in pre-space flight Moclin culuture, women were not desirable by the vast majority of Moclins and those males that desired females were ostracized to the point of extreme closeting of their true sexual urges. Trans-sexual surgeries were eventually developed and refined so that the attached male genitalia was functionally indistinguishable from a natural one.

If so, it would explain the rarity in the 2400s as in order to possibly have a girl, you would have to have a taboo love of a man and a woman Moclan that produced offspring which would have a greater chance of female genetics. If we assume that the Y chromosome is dominant, then the following parings are possible YY-YY, YY-YX, YY-XX, YX-XX. In the first, all resulting children are YY Males. In the second, half the children are YY Male and half are YX Male. In the third, half of the children are YX Male and Half are XX Female, and in the final one, one quarter are YX Males, and three/quarters are XX Female. This means that if we start with an even number of parings, the ration of men to women in the next generation is 11-5 with all things being equal, and with more generations, these chances are likely to go up.

This uneven gender birth ratio is bad on it's own, but if being female is a big taboo in Moclin Society, and heterophobia is as common as Klyden's display of it, then it would increase the rate of appearence of a naturally born female to much higher territory. Even on Earth, enforced gender preferences are more likely to cause greater troubles down the line. We can observe that under the One Child Policy, China's population stagnated as families perfered boys to girls and would often abort female fetus or abandon them to the their deaths. This culling would further inflate the numbers... and given the surgery and the fact that Klyden wasn't aware he was really a she at birth until he was seen by a non Moclin Medical doctor, who could identify the signs of the transition, it's quite likely that Moclin children aren't reported as female to male trans all that often. Most who know who they are don't want to speak about it because it might make them less desirable for a mate.

And as to a male-female differences being more nuanced to humans than Moclins, consider Moclins are more reptillian and thus have no mammalries, and that the reason that Klyden and Bortas' speaking is so stilted and formal is attributed to the fact that English isn't their native language, it could be this very concept that confused the issues for Moclins and Humans upon first Contact. Among the delegation in Earth's First Contact package about their culture was the Ancient Classic movie "Kindergarten Cop" which has the famous scene in which a Kindergartener explains to Arnie the difference between boys and girls (Moclins seem to love literature and Bortas learned about how differences could be strengths from Rudolph the Red Nosed Reindeer, so Moclins learning genders from Kindergarten Cop is perfectly possible in the Orville-verse). The Moclins probably missed the humor, and used the words to describe their own sexual society... and the fact that sex is a taboo subject for all of them, it could be that's where they left the discussion.

The fundamental difference between the gametes in "typical" Earth sexual reproduction is that the egg contains the full compliment of organelles required to be a living cell that can reproduce, while sperm are trimmed down to contain only the bare necessities needed to reach an egg.

Fundamentally someone needs to bring enough organelles to function once fertilization occurs. But there's no reason that has to be just one side.

Consider a species which gestates via a common sperm pool. Each sperm contains some of the organelles needed to function, but not all. If the sperm fuze (fertilization), they pool their resources (organelles) in order to try to become the winning ovum. It then engages in a hostile takeover of other sperm in the pool, seeking to acquire all of the organelles that its pair of sperm lacked.

In effect, it's a cellular level equivalent to how some sharks reproduce. Some sharks will have a litter of 4 sharks, but the womb does not contain enough resources for 4. The biggest most aggressive shark kills and eats the other sharks and their yolk sacks and uses that to fuel its own growth. Thus, for those species, every shark born is already a murderer, having killed several of its siblings in a fight to the death.

The fun part of the design will be trying to define the equilibrium which prevents this solution from degenerating into the more traditional egg and sperm pattern. There may be a Nash equilibria in their reproductive tactics which prevent them from choosing to go to this traditional approach.

I think you could use some kind of jellyfish with the ability to reproduce by fragmentation (https://en.wikipedia.org/wiki/Fragmentation_(reproduction) ) like a hydra, but bigger, like a Nomura jellyfish, or maybe would be better a kind of giant annelid worm. However, before evolving this reproduction this species used to reproduce with males and females, they still have the characteristics of male to be able to fecundate, sometimes they do with females of other similar species, because it is a gene that they have not lost, they only remain males because the first to evolve the characteristics to this type of asexual reproduction were male.
if you want your species to be more like an aware one, well... with time and necessity your nervous system could came to develop the equivalent of a brain, i guess, and from time to time they allow themselves to cross with other species with which they can hybridize, to have genetic variability.