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This paper proposes a modular method, called generalized product, of combining two coalgebraic hybrid logics in a parallel but non-compositional way. This is a coalgebraic generalization of a hybrid extension of product of modal logics. Our method, however, covers not only the combination of the same-type logics but also the combination of two different-type logics, e.g., graded hybrid logic and non-monotone hybrid logic. Moreover, we provide general strong completeness results for generalized products of coalgebraic hybrid logics with generic criteria.