 In Coniglio and Figallo 2015, Coniglio and Figallo extended the idea of meta-fibring (that is, algebraic fibring of formal sequent calculi) to hypersequents, which allows preserving even stronger meta-properties of the logics being combined. Hypersequents, which are finite multisets of ordinary sequents, constitute a natural generalization of the proof-method of sequents and turn out to be a suitable tool for presenting cut-free Gentzen-type formulations for several non-classical logics.