$\mathcal{N}=4$ supersymmetric multiparticle systems based on indecomposable multiplets

We construct new multiparticle models of $\mathcal{N}=4$ supersymmetric mechanics with spin degrees of freedom by employing nonlinear indecomposable supermultiplets $(\mathbf{1},\mathbf{4},\mathbf{3})\supset +(\mathbf{4},\mathbf{4},\mathbf{0})$. These systems are proper deformations of those associated with the standard irreducible $d=1,\mathcal{N}=4$ multiplets. In this way we find a new $\mathcal{N}=4$ supersymmetric generalization of U$(2)$-spin rational Calogero system invariant under $d=1$ superconformal group OSp$(4\mathrm{\mid }2)$. One more deformed model reproduces $\mathcal{N}=4$ supersymmetric U$(2)$-spin hyperbolic Calogero system, up to a shift of the Hamiltonian by some U$(1)$ generators.