Lateraling from lower BB to top BB

Hey all — I'm an incoming intern at a lower BB this summer (not Deutsche or UBS). I am considering leveraging my summer internship and lateraling to a more top BB (GS, JPM, MS) for better PE placement, given that PE firms seem to care about brand prestige.

Is it actually worth it? If so, how do you re-recruit without jeopardizing receiving a full-time offer at the lower BB? Would love to hear any stories. Thanks