  Intertwining relations for $N$-particle Calogero-like models with internal
degrees of freedom are investigated. Starting from the well known
Dunkl-Polychronakos operators, we construct new kind of local (without exchange
operation) differential operators. These operators intertwine the matrix
Hamiltonians corresponding to irreducible representations of the permutation
group $S_N$. In particular cases, this method allows to construct a new class
of exactly solvable Dirac-like equations and a new class of matrix models with
shape invariance. The connection with approach of multidimensional
supersymmetric quantum mechanics is established.
