Marginal treatment effect methods are widely used for causal inference and policy evaluation with instrumental variables. However, they fundamentally rely on the well-known monotonicity (threshold-crossing) condition on treatment choice behavior. Recent research has shown that this condition cannot hold with multiple instruments unless treatment choice is effectively homogeneous. Based on these findings, we develop a new marginal treatment effect framework under a weaker, partial monotonicity condition. The partial monotonicity condition is implied by standard choice theory and allows for rich heterogeneity even in the presence of multiple instruments. The new framework can be viewed as having multiple different choice models for the same observed treatment variable, all of which must be consistent with the data and with each other. Using this framework, we develop a methodology for partial identification of clearly stated, policy-relevant target parameters while allowing for a wide variety of nonparametric shape restrictions and parametric functional form assumptions. We show how the methodology can be used to combine multiple instruments together to yield more informative empirical conclusions than one would obtain by using each instrument separately. The methodology provides a blueprint for extracting and aggregating information about treatment effects from multiple controlled or natural experiments while still allowing for rich heterogeneity in both treatment effects and choice behavior.