Hi there, welcome. Well, there is no cap on how active young kids can be. In fact, they should exercise daily. My boys have some days where much of their day is spent doing physical activity! It's often fun stuff like a day at the pool, long bike rides to the park where they run around and play and then a long bike ride home, etc. My boys play sports and I'm that crazy parent that lets them explore what they want to do and they often play a couple sports at the same time. My boys are 8 and 9. Both my boys swim on a year round swim team, one plays soccer too and the other plays Fall baseball and flag football this sports season. The biggest challenge to multiple sports at a time in one season is scheduling. You don't want to short change one team for another. So, I work hard to schedule things so they don't conflict. I find out when games are for each sport and make sure they are different times. My son has baseball on Saturdays and flag football on Sundays. Practice is also on different days. So, we can do it. If it were on the same day, he'd have to choose which one as it is not fair to try to do both and not be there when the team needs him-- if that makes sense.
But my boys enjoy sports. I think it is like when we try to get in shape. You have to enjoy the method of activity that you choose in order to stick with it. So, make sure he is part of the decision process and give him lots of encouragement. He has to be happy doing it or it will feel like torture to him. And don't forget about simple outside play for exercise. good luck