The double distorted perovskites Ca(Cu3-xMnx)Mn4O12 (x = 1, 1.25, 1.5 and 2) exhibit a paramagnetic-to-ferrimagnetic transition at a temperature decreasing from TC = 280 K for x = 1 down to TC = 163 K for x = 2. In the latter compound, a reentrant-like spin-glass state emerges around Tg = 70 K. For each composition, the isothermal entropy change /DeltaSM was derived from magnetic measurements recorded up to 9 T. The obtained /DeltaSM(T) curves exhibit a broad and dissymmetric distribution, leading to high values of refrigerant capacity. The impact of the x value on the magnetic and magnetocaloric properties is addressed in detail, taking into account the various spin interactions present in these compounds.