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This paper describes TSAT++, an open platform which realizes the lazy SAT-based approach to Satisfiability Modulo Theories (SMT). SMT is the problem of determining satisfiability of a propositional combination of T-literals, where T is a first-order theory for which a satisfiability procedure for a set of ground atoms is known. TSAT++ enjoys a modular design in which an enumerator and a theory-specific satisfiability checker cooperate in order to solve SMT. Modularity allows both different enumerators, and satisfiability checkers for different theories (or combinations of theories), to be plugged in, as far as they comply to a simple and well-defined interface. A number of optimization techniques are also implemented in TSAT++, which are independent of the modules used (and of the corresponding theory). Some experimental results are presented, showing that TSAT++, instantiated for Separation Logic, is competitive with, or faster than, state-of-the-art solvers for that very logic.