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We optimize the magnetic and structural properties of Ni(Co,Cu)MnSn Heusler alloys for the magnetocaloric effect (MCE) by means of density functional theory combined with Monte Carlo simulations of a classical Heisenberg model. NiMnSn alloys show a drop of magnetization at the martensitic phase transition, which leads to the inverse MCE. We find either disordered or frustrated magnetic configurations directly below the martensitic transition temperature. However, the jump of magnetization at the magnetostructural transition is small as the austenite is in a ferrimagnetic state and not fully magnetized. For Co and Cu substitution, the structural phase transition temperature shifts to lower temperatures. In particular, Co substitution is promising, as the magnetization of the austenite increases by additional ferromagnetic interactions, which enhances the jump of magnetization.