Princeton SCEA/Brown ED/PLME

Hey so I have a few questions. My number one choice for college would be the Brown PLME program. I am 100% aware that the chances of getting into this program are minuscule. And, I’m also aware that if I apply ED and get into Brown but not PLME I am bound to Brown. My second choice after the PLME program would be Princeton and then third would be Brown w/o the PLME. So, I’m wondering would it be better to apply to Brown ED and take the risk of not getting into the program (but have a higher chance of getting into Brown) or apply to Princeton SCEA and apply to Brown and PLME RD. Basically, does applying to Brown ED increase chances of getting into PLME? I think both schools are amazing but I’m wondering if applying to Princeton SCEA would be stupid because I’d be dampening my chances at PLME. Is that the case, or is there not really much of a difference? Thanks in advance to anyone who has some input!