If you talk to any college/professional coach or any sport and ask them if kids should focus on one sport to get better at it or play several different sports I think they'd all say it's better to play several sports.
Each sport generally requires different motions and abilities so you're not overworking one muscle or ligament and as a bonus you're also learning new abilities that you can use in the sport you care most about.
If I were a high school football coach, I'd greatly "encourage" my safeties to play baseball, specifically as outfielders, my receivers to run track to work on explosion of the line, and my linemen and linebackers to all wrestle to learn the best techniques to use their body weight and hands in 1 vs 1 competition.
I wouldn't want my QB to be a pitcher because it may hurt his arm but more and more middle infield training and learning how to throw from different arm angles and platforms is becoming an important tool to have.
A lot of quarterbacks were pitchers. Probably don't want to pitch during football season though.
I think the biggest thing about playing 3-4 sports is the fact that you are in competition mode all year. And, you get to compete with your buddies all year.