The existence of a compensator is considered which simultaneously renders a given r-tuple of m-input p-output linear dynamical systems internally stable. An extension of the classical pole placement and stabilization problems is investigated. It is shown that, if \(r\cdot \min (m,p)\leq m+p\), the simultaneous partial pole assignment problem can be analyzed via interpolation methods, and one obtains a semialgebraic parametrization of the partially pole assignable r-tuples of the plants. If \(r\cdot \min (m,p)>m+p\), the simultaneous partial pole assignment problem can be analyzed via transcendental methods of the type introduced in the paper.