In this talk, I will present an extension of the mosaic method to the case of logics arising from the combination of linear tense operators with an "orthogonal" S5-like modality. The technique will be applied to obtain a proof of decidability, a proof of completeness for the corresponding Hilbert-style axiomatization and to develop a mosaic-based tableau system. (From a joint work with Carlos Caleiro and Luca Viganò.)