Exactly solvable three-body systems with internal degrees of freedom

The approach of multi-dimensional SUSY quantum mechanics is used in an expl icit construction of exactly solvable three-body (and quasi-exactly-solvabl e N-body) matrix problems on a line. From intertwining relations with time- dependent operators, we build exactly solvable non stationary scalar and 2 x 2 matrix three-body models which are time-dependent extensions of the Cal ogero model. Finally, we investigate the invariant operators associated wit h these systems.