Any college / pro scout or coach will quickly tell you how much they like baseball players that also play other sports. Makes a better all around athlete. It's getting harder and harder to do, even at the HS age.
My travel team consists of kids all playing JV Ball. We've played 1 tournament before HS season started. Another a few weeks later (both local). We played one this month (local again). We'll play one next month. Their JV season is done in early May. We'll play a week long (World Wood Bat) in June, and a weekend tourney before that. We'll play one weekend tourney July 4th weekend, and they are off all of July. I'll run my tryouts again in late late July Early August. We'll play a couple of tournaments in September and one in early October. Those kids on my team are then required to shut down baseball (no throwing / hitting etc) for a minimum 45 days. In the past it's usually lasted until after Christmas. Then we start Winter workouts. It helps that most all play basketball. Those who don't (and even those who do) usually are working out (running / strength training). In other words, not doing anything baseball related.
What kills me is if you ask a Coach if it's a good idea to lift weights,everyday, that target the same muscles, of course they will say no. But they are fine with kids throwing, pitching and hitting everyday without taking a break.