HOW LIKELY WILL I GET GS/JPM/MS FT THIS YEAR?

Hey guys, I come from non-target and we don't get BB NYC postings.

I struck luck and was able to land BB (UBS/Citi/DB) IBD NYC offer for the summer. I really want GS/MS/JPM or even CS NYC for full time. What are the chances of me being able to leverage the lower tier BB offer for the top tier BB offers, given that my school isnt a target?

Does it happen often?