We provide technical details for both a fibring and an independent combination of normal and a non-normal logics underlying a normative multi-agent system (normative MAS). Such combinations lead to different levels of expressiveness of the system. Based on the fibring, we give a possible structure for a combined model checker for the MAS. The independent combination provides: (i) an ontology of pairs (mental configuration-visible behavior), which can be understood as a structural account to supporting non-monotonicity; and (ii) a logics where to write and test the validity of a wider set of well-formed formulas.Sociedad Argentina de Informática e Investigación Operativa