This is considered one of the difficult PRT challenges. A baseball game is even worse than a train station. You could have a very long spur at a high capacity station, or even a spur with its own spurs where cars can presumably move in and back out. You would also have to have fancy algorithms to create gaps in traffic going past the big station to accept all the traffic. Ideally it would leave in bunches, sort of like trains but uncoupled.

Or you would of course, have to have long waits at such stations from time to time. Which is what we have now with shared transit, after all.