Gosh, I see the University Near Here has adopted a new motto for its website:
Welcome to UNH, a flagship public research university on the edge of possible.
I think more standard usage would suggest a "the" before "possible": on the edge of the possible.
But even then, it's eye-rolling. What could that conceivably mean?
UNH goes right up to the edge… why would it do that? Stop! Come back!
Any chance it could trip over the edge of the possible into … the impossible? Probably not. By definition.
Welcome to UNH, a flagship public research university where people are paid good money to come up with meaningless, intelligence-insulting slogans for our web page.
OK, so it's not the best marketing, but it has the advantage of truth.