The exogenous semantic approach for enriching a given base logic was introduced by Mateus e Sernadas in order to obtain an exogenous quantum logic that extends classical propositional logic (CPL). In this enrichment we can distinguish two important intermediate steps, globalization and probabilization. In this work we propose an algebraic study of Exogenous Global Propositional Logic (EGPL) and Exogenous Probabilistic Propositional Logic (EPPL). We start by introducing a many-sorted approach to algebraizability, suitable for reasoning about logics that, like EGPL and EPPL, have rich (many-sorted) languages. We show that EGPL over a base logic L, EGPL(L), is always algebraizable. Moreover, when L is also algebraizable, we can recover the algebraic counterpart of L using behavioral reasoning. We also show that EPPL(CPL) is algebraizable and present an equivalent algebraic semantics for it. Joint work with Carlos Caleiro.