Can i move company before Oct 1?

Company A has applied for my H1b with premium processing on May 19. I expect it to be approved by June.
Can company B also do premium processing for my H1B and I can join it by July if it is approved? I’m on STEM OPT and have a year left, and h1b can come in effect from October.

My guess is if it is not allowed, then when company B applies, it won’t be approved? What am I missing?