Materials with magnetic anisotropy can serve as a model object for exploring the multicaloric effect because their thermodynamic state alterations can be achieved either through the application of a magnetic field H or/and by mechanically rotating the sample in the magnetic field using torque τ. In such materials, the total entropy change __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__Δ S T arises from two distinct contributions: (1) the conventional magnetocaloric effect (MCE) or paraprocess __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__Δ S m and (2) the rotational MCE __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__Δ S φ . In this manuscript, using molecular field model which enables a separation of contributions to the total entropy change __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__Δ S T from conventional __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__Δ S m and rotational __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__Δ S φ , we have determined cross-coupling multicaloric coefficients __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__ χ τ , H = ∂τ ∂H T , θ and __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__ χ H , τ = - ∂m ∂θ T , H for anisotropic magnetic materials and show that they satisfy the basic thermodynamic identities. We also confirmed that the total multicaloric effect in the material with magnetic anisotropy can be accurately expressed as the sum of the individual magnetocaloric effects induced by separate application of the H and τ, minus the magnetic entropy change arising from thermodynamic cross-coupling between the subsystems of the solid: __-mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"-__ Δ S T = Δ S T , τ H + Δ S T , H θ - Δ S coupling .