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We present a novel approach for generating interaction combinations based on SMT constraint resolution. Our approach can generate maximal interaction coverage in the presence of general constraints as supported by the underlying solver. It supports seeding with general predicates, which allows us to combine it with path exploration such that both interaction and path coverage goals can be met. Our approach is motivated by the application to behavioral model-based testing in the Spec Explorer tool, where parameter combinations must be generated such that all path conditions of a model action have at least one combination which enables the path. It is applied in a large-scale project for model-based quality assurance of interoperability documentation at Microsoft.