Please help settle an argument between myself and my son. I believe that John/Jane was the only time traveler being manipulated by the Agency, in order that they may not change the future. Nowhere in the movie do you see anyone else time traveling. It is implied, but never seen. The same is in the short story, "All you Zombies".
In the short story, although you never "see" anyone else time-travelling, it is very strongly implied that the narrator is only one of many time agents:
2300-VII-12 Aug 1985-Sub Rockies Base: I woke the duty sergeant, showed my I.D., told the sergeant to bed him down with a happy pill and recruit him in the morning. The sergeant looked sour but rank is rank, regardless of era; he did what I said—thinking no doubt, that the next time we met he might be the colonel and I the sergeant. Which can happen in our corps. "What name?" he asked.
I wrote it out. He raised his eyebrows. "Like so, eh? Hmm—"
"You just do your job, Sergeant." I turned to my companion. "Son, your troubles are over. You’re about to start the best job a man ever held—and you’ll do well. I know."
" ‘But’ nothing. Get a night’s sleep, then look over the proposition. You’ll like it."
"That you will!" agreed the sergeant. "Look at me—born in 1917—still around, still young, still enjoying life." I went back to the jump room, set everything on preselected zero.
2301-V-7 Nov 1970-NYC-"Pop’s Place": I came out of the storeroom carrying a fifth of Drambuie to account for the minute I had been gone. My assistant was arguing with the customer who had been playing "I’m My Own Granpaw!" I said, "Oh, let him play it, then unplug it." I was very tired.
It’s rough, but somebody must do it and it’s very hard to recruit anyone in the later years, since the Mistake of 1972. Can you think of a better source than to pick people all fouled up where they are and give them well-paid, interesting (even though dangerous) work in a necessary cause? Everybody knows now why the Fizzle War of 1963 fizzled. The bomb with New York’s number on it didn’t go off, a hundred other things didn’t go as planned—all arranged by the likes of me.
In the movie the existence of a time agency implies more than one agent, though none are shown.
This is unclear in the movie. It is implied that, even if there were additional agents, at least John is special, as evidenced by this bit by Mr. Robertson:
Understand you are more than an Agent. You're a gift given to the world through a Predestination Paradox. You're the only one free from history, ancestry.
So John is the only agent in a closed time loop. I suppose there could be other, less extraordinary agents, but we never see one.
However, in the short story, All You Zombies, it's clear there are other agents. Joe L. answer's provides some pretty strong evidence, but if there was any doubt, one of the closing paragraphs from the story is pretty explicit that there are many recruits, which are definitely NOT incarnations of John:
I dictated my report; forty recruitments all okayed by the Psych Bureau - counting my own, which I knew would be okayed.
It is mentioned by that barkeeper this:
I'm a Temporal Agent, one of 11.
According to this information, he is not the only one.