Approaching reconfigurable systems as structured transition systems, where the states are models in a given institution, is a methodological approach pursued in [17]. The versatility of this approach lies in the assumption that the logic used for configurations can be chosen based on the nature of the system configurations to be developed. Technically, this is supported by using parametric methods to build modal logics on-demand (e.g. [12, 18]). In this paper, we go a step further by assuming that configurations can be governed by different logics, even within the same reconfigurable system. We operationalize this principle for the formal specification of systems by enriching and reshaping the formalism many-logics modal logic [10] within the theory of institutions and by introducing a number of relations between models that preserve logical properties.