My son just played his first year of Pony Baseball (he finished up the week before his 4th birthday). Pony is similar to Little League, but with slightly different rules (or at least that's what other moms told me). In Pony, the distance between bases gets bigger as kids get older. Younger kids (t-ball) don't keep score; everyone bats and everyone fields. They offer both fall and spring ball.
I don't plan to put my son in fall ball unless he begs me to AND shows enough skill to make it worthwhile. Otherwise, I'd rather stick to baseball in the spring and have him try out soccer in the fall so he has a chance to experience other things. When he's old enough, I'd also like him to try basketball and see what he likes the best.
My personal opinion... if you want to add one extra team, go for it, since he loves it so much. But if he's playing on three teams a year, I think he'll get burned out - and so will you. I also keep hearing about how many kids (mostly high schoolers, but sometimes even younger) are having a lot more sports-related injuries and surgeries than ever before because of overuse. Kids bones are still developing and they need an offseason so they have a chance to rest.