I personally do not push my students to do a ton of entries. Two sets of single dances per style plus scholarship and championship.
That is a ton for some of us... or at least, more than we do!
For budget reasons, I usually restrict to 15 dances (pro charges per dance, plus expenses). My preferred way to distribute this would be all 5-dance multis, but thanks to pre-reqs, I usually have to burn 5-10 of those dances on singles. If I add my second style, the distribution goes to something like 10 (primary style) + 6 (second style).
Stamina-wise, I'm good to go for much more. Assuming a typical schedule, I could quite easily handle 10-15 singles, two 3-dance championships, and 2 5-dance events... but I never have that may options, and couldn't afford it even if I did, unless it was the only comp I did all year. I'd rather dance less at each one, but go to more comps - that gives me the chance to learn, improve, change things around, etc.
Pro maxes out at about 5 students per style, with everyone dancing between 9 and 18 dances. And when latin and standard are on the same day, it's about 6-7 students total. Any time he's tried to go above that number, it's been a bit of a disaster for those of us that have more athletically demanding choreo or dance in the evening session. He's admitted that (not to everyone, naturally), and is more careful about how many he takes when the open ladies are attending than he was in the past.
Edited to add: there is a local pro here who takes great pride in doing the ironman thing - as many entries as possible. He doesn't leave the floor... and he's barely moving by the end, let alone actually dancing. His students are absolutely free to do that and it seems to work for them, but there's a reason why I don't dance there. (Well, several... but you get the idea.)