This paper presents a procedure for the verification of multi-process systems based on considering a series of underapproximated models. The procedure checks models with an increasing set of allowed interleavings of the given set of processes, starting from a single interleaving. The procedure relies on SAT solvers' ability to produce proofs of unsatisfiability: from these proofs it derives information that guides the process of adding interleavings on the one hand, and determines termination on the other. The presented approach is integrated in a SAT-based Bounded Model Checking (BMC) framework. Thus, a BMC formulation of a multi-process system is introduced, which allows controlling which interleavings are considered. Preliminary experimental results demonstrate the practical impact of the presented method.