Abstract Multiferroic materials with strong coupling between different degrees of freedom are prone to exhibit giant multicaloric effects resulting from the application or removal of diverse external fields. These materials exhibit a synergic response to the combined action of two fields when the monocaloric effects are both conventional (or both inverse), while a non-synergic response occurs when one of the monocaloric effects is conventional and the other is inverse. In all cases, the multicaloric properties (isothermal entropy and adiabatic temperature changes) do not result from the simple addition of the corresponding monocaloric quantities because there is a contribution from the interplay between degrees of freedom (cross-coupling term). In this paper, we analyse in detail the contribution of the cross-coupling term to the multicaloric entropy values obtained for both synergic and non-synergic multicaloric materials. We first introduce basic thermodynamic concepts accounting for the multicaloric effects, and next the contribution from the cross-coupling term is illustrated via several model examples. We finally analyse the realistic situation for two prototype materials with synergic and non-synergic multicaloric effects.