Model generation operations are important artifacts in MDE applications. These approaches can be used for model verification, model finding, and others. In many scenarios, model transformations can as well be represented by a model generation operation. This often comes with the advantage of being bidirectional and supporting increments. However, most part of model generation approaches do not target several operation kinds, but narrower scenarios by mapping the generation problem into solver specific problems. They are efficient, but often don’t have a supporting framework. In this paper, we present an approach and framework that allows to specify and to execute model operations that can be represented in terms of model generation operations. We first introduce a model search layer that can be used with different solvers. We illustrate this layer with a driving example implemented using Alloy/SAT solver. On top of this, we introduce a transformation layer, which specification are translated into the model search layer, independently from any solver. The solution is natively bidirectional, incremental and it is not restricted to one-and-one scenarios. The approach is illustrated by two use cases and with 3 different scenarios, backed by a full, extensible and free implementation.