An extension of the work of Baker and Blankenbecler is presented in which 2 → 2, $2\to n$, and $m\to n$ particle amplitudes satisfy unitarity, including both elastic and inelastic terms. Disconnected parts of the $m\to n$ amplitudes are, however, not included. Dynamical applications of the model to the unitarization of meromorphic Born terms are briefly discussed. In particular, pole degeneracies are shown to be broken, and factorization of output resonance poles is proved.

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