Yet another $S$-unit variant of Diophantine tuples

We show that there are only finitely many triples of integers $0<a<b<c$ such that the product of any two of them is the value of a given polynomial with integer coefficients evaluated at an $S$-unit that is also a positive integer. The proof is based on a result of Corvaja and Zannier and thus is ultimately a consequence of the Schmidt subspace theorem.