Well when my friends and I sit around and talk about jacking off this often comes up. Actually no, no it doesn’t.
So I’m sure experiences will vary a lot but for most guys the answer is, once. It’s not because they couldn’t cum more if they really wanted to, it’s just we are lazy fuckers and once our balls are emptied we mostly just want to lie back and bliss out. This is a reason why in general love-making the ‘She cums first’ rule is so powerful, because we don’t give a shit about anything once we do.
Penises go into a ‘refractory’ period after cumming which means without some extra help, such as a cock ring or viagra, they’ll go soft and stay that way for a while.
So this is, for most guys, quite markedly different from a woman’s multiple orgasms. Women have what’s described as an ‘orgasmic plateau’ where once they cum they don’t have the full drop in response that men do. We basically have to work back to orgasm from the starting point (except we aren’t horny the next time around) whereas women often (not always) stay pretty horny after cumming (you stay even hornier not cumming, just saying), and so that enables women to get back to more orgasms much faster and more easily than men. For instance I’ve lost count many a time making my wife cum, but it was often in high teens and into the 30+ arena in rare sessions – you can compare that to my results below.

And yes, that graph totally has a denial option on for the women… love it.
I’ve done things in the interest of science for a long time, so of course I wondered the same as the OP, And having a handy penis to experiment with (mine, before you ask) I used to do regular research. I’d find that I could cum four or five times before I couldn’t get an erection again. So that’s in a row, with a few minutes between each. But it’d get harder to get there each time.
But that was when I was a young lad. Nowadays I’d not try to go for more than two,and most of the time it’s just one. The exceptions is if they are ruined, when I can get to four or five still (fucked up but hot),
The other interesting fact is you do eventually run ‘dry’ which is a mindfuck. So your first ejaculation is the biggest, but actually the second can be nearly as large, or at least substantial (which is always surprising). By orgasm 3 your balls are definitely draining, it’s just the remnants, And on the fourth it’s just what your prostate has managed to churn up while you’ve been wanking, little more than a dribble. By the fifth, nothing cums out. YMMV