Scenario-Based Programming is a methodology for modeling and constructing complex reactive systems from simple, stand-alone building blocks, called scenarios. These scenarios are designed to model different traits of the system, and can be interwoven together and executed to produce cohesive system behavior. Existing execution frameworks for scenario-based programs allow scenarios to specify their view of what the system must, may, or must not do only through very strict interfaces. This limits the methodology's expressive power and often prevents users from modeling certain complex requirements. Here, we propose to extend Scenario-Based Programming's execution mechanism to allow scenarios to specify how the system should behave using rich logical constraints. We then leverage modern constraint solvers (such as SAT or SMT solvers) to resolve these constraints at every step of running the system, towards yielding the desired overall system behavior. We provide an implementation of our approach and demonstrate its applicability to various systems that could not be easily modeled in an executable manner by existing Scenario-Based approaches.