When is IV identification agnostic about outcomes?

Many identification results in instrumental variables (IV) models hold without requiring any restrictions on the distribution of potential outcomes, or how those outcomes are correlated with selection behavior. This enables IV models to allow for arbitrary heterogeneity in treatment effects and the possibility of selection on gains in the outcome. I call this type of identification result "outcome-agnostic", and provide a necessary and sufficient condition for treatment effects to be point identified in an outcome-agnostic manner when the instruments and treatments take a finite number of values. The condition generalizes the well-known LATE monotonicity assumption, and unifies a wide variety of other known IV identification results. The result also yields a brute-force approach to revealing all selection models that allow for point identification of treatment effects, and then enumerating all of the identified parameters within each selection model. Though computationally intensive, the search uncovers several new IV identification results even in simple settings.