Abstract
The super-additivity of quantum channel capacity is an important feature of quantum information theory different from classical theory, which has been attracting attention. Recently a special channel called ``platypus channel'' exhibits super-additive quantum capacity when combined with qudit erasure channels. Here we consider the ``generalized platypus channel'', prove that it has computable channel capacities, such as both private and classical capacity equal to 1, and in particular, the generalized platypus channel still displays the super-additivity of quantum capacity when combined with qudit erasure channels and multilevel amplitude damping channels respectively.