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We investigate for which multipliers \\theta : \\mathbb{B}^m \\raro \\cll(\\cle, \\cle_*) the quotient module \\clh_{\\theta} is similar to H^2_m \\otimes \\clf for some Hilbert space \\clf, where M_{\\theta} is the corresponding multiplication operator in \\cll(H^2_m \\otimes \\cle, H^2_m \\otimes \\cle_*) for Hilbert spaces \\cle and \\cle_* and \\clh_{\\theta} is the quotient module (H^2_m \\otimes \\cle_*)/ {clos} [M_{\\theta}(H^2_m \\otimes \\cle)]. 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