the problem about submitting later is that the longer you wait, the longer it takes for them to check your application. For example, i submitted my application within the first day it was open, within the first hour, actually. It took them only 24 hours to check it. My friend submitted 2 weeks later, - it took them 3-4 weeks. During the application there will be a spot where you will be able to select that you have future MCAT date, and thats fine. The factor that takes the longest is the verification of all your college courses, - in the pick of the season it can take up to 5-6 weeks. So, it is much smarter to submit june 1st (or whatever the EARLIEST date you can) with one school selected, let them verify everything. And then, once your MCAT test results go through, you can add as many school as you like, thats fine.