This paper presents FaMSA, an efficient method to boost 3D scan registration from partially known correspondence sets. This situation is typical at loop closure in large laser-based mapping sessions. In such cases, scan registration for consecutive point clouds has already been made during open loop traverse, and the point match history can be used to speed up the computation of new scan matches. FaMSA allows to quickly match a new scan with multiple consecutive scans at a time, with the consequent benefits in computational speed. Registration error is shown to be comparable to that of independent scan alignment. Results are shown for dense 3D outdoor scan matching.