We develop a general thermodynamic framework to investigate multicaloric effects in multiferroic materials. This is applied to the study of both magnetostructural and magnetoelectric multiferroics. Landau models with appropriate interplay between the corresponding ferroic properties (order parameters) are proposed for metamagnetic shapememory and ferrotoroidic materials, which, respectively, belong to the two classes of multiferroics. For each ferroic property, caloric effects are quantified by the isothermal entropy change induced by the application of the corresponding thermodynamically conjugated field. The multicaloric effect is obtained as a function of the two relevant applied fields in each class of multiferroics. It is further shown that multicaloric effects comprise the corresponding contributions from caloric effects associated with each ferroic property and the crosscontribution arising from the interplay between these ferroic properties. This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'