  Multivalued treatment models have typically been studied under restrictive
assumptions: ordered choice, and more recently unordered monotonicity. We show
how treatment effects can be identified in a more general class of models that
allows for multidimensional unobserved heterogeneity. Our results rely on two
main assumptions: treatment assignment must be a measurable function of
threshold-crossing rules, and enough continuous instruments must be available.
We illustrate our approach for several classes of models.
