In general, by fibring two or more fragments of a given logic, the resulting logic is weaker than the original one, because some important meta-properties of the connectives are lost after the combination process. The lack of such meta-properties avoids the creation of some interactions between conectives from its combination (for instance, distributivity between conjuction and disjunction). In this talk, the question of recovering a logic system by combining fragments of it will be addressed. Specifically, categories of multiple-conclusion consequence relations and sequent calculi will be introduced in such a manner that, in several cases, a logic can be recovered by fibring (in these categories) its fragments. This process is called meta-fibring. The key feature of these categories is a notion of morphism stronger than usual, which preserve several meta-properties of the consequence relations. Soundness and completeness preservation by meta-fibring (wrt algebraic semantics) are obtained.