I am currently on a waitlist for a DO school, I was wondering if I should/am allowed to re-apply for the next cycle considering that I have submitted an LOI for this school.
You are allowed to start working on and submit an app for the new cycle, though AACOMAS is not very time sensitive and waiting a few weeks should be fine, especially if you have already thought about and made modifications to your written materials.
I am currently on a waitlist for a DO school, I was wondering if I should/am allowed to re-apply for the next cycle considering that I have submitted an LOI for this school.
You should be reapplying, because as of right now, you're rejected.
Just apply to a throw away school, to get verified. You can wait until later in the cycle to fully apply. But you should also be filling any holes in your app.