Depends on the horse's fitness and experience and the height of the jumps, but also what you're aiming to achieve.
When I take the ponies out to training shows they might do 2 rounds (crosspoles/40cm as a warmup and then the 60/70/80cm), but being youngsters and only exercised once a week, I certainly wouldn't ask them to go round 3 times! When I'm doing training shows with Jam (we do anything between 90cm and 1.10m) we only do the one class - unlike with the ponies, this is not a fitness issue, but there's no logical reason for us to do two classes, so we don't! My boss's horses only ever jump 1 class in a day - so a maximum of 2 rounds if they get into a jumpoff.
If you're doing clear-round classes, personally I don't see the benefit of going round the same height more than once, if the first round went well. If the first round was rubbish I'd definitely do a 2nd, and iron out our mistakes. If I only did 1 round in that class, I'd probably do the next height up as well. If I'd done 2 rounds in the first class, I wouldn't then go on to jump a bigger class. I don't see the point in going round 3 times in one day.
ETA most shows here are official/affiliated and the only shows that do clear-round type classes are "training shows" - these are mostly done by RS riders on RS horses, and horse-owners without a competition license, and these classes always state in the rules that no horse/pony can jump more than 3 times in the day.