It’s tricky to give more than one or two enough time to keep the relevant skills/fitness at a level to get the most out of them.
Years ago it was all about climbing and hillwalking for me, now it’s pretty much all biking and the odd climbing trip isn’t great because I haven’t got the confidence anymore. Similarly if you’re only going to get out on your bike once every few weeks I don’t think you get as much out of it ‘cos you’re just not as fit and on the ball. So yes, I think you can have too many hobbies if you want to do any of them to a reasonable level.
EDIT: Wot Grumm said basically!