It has been shown that a generic r-tuple of m input p output dynamical systems is simultaneously stabilizable (pole assignable) if r < m + p and the McMillian degrees of the systems are not too different. This result improves the currently known upper bound: r less than or equal to max(m, p) on the number of plants. In the case r less than or equal to max(m, p), an upper bound on the degree of the simultaneous pole assigning compensator has also been derived, which improves the bound obtained by Ghosh and Byrnes in 1983.