You could impose the standard (Angrist and Imbens) monotonicity assumption, but this requires assuming that all people respond more to one instrument than another. That is unlikely to hold in a heterogeneous population in most settings.

Mogstad, Torgovitsky, and Walters (2021) provide an alternative, less restrictive "partial" monotonicity assumption: here, all you need is that each instrument weakly increases treatment probability for each individual. With that assumption, you can then estimate two-stage least squares as usual