The present paper proposes two new methods for constructing polyphase asymmetric zero-correlation zone (A-ZCZ) sequence sets. In previous studies, the authors proposed methods for constructing quasi-optimal polyphase A-ZCZ sequence sets using perfect sequences and for constructing optimal polyphase A-ZCZ sequence sets using discrete Fourier transform (DFT) matrices. However, in these methods, the total number of sequences in an A-ZCZ sequence set cannot exceed the period of the perfect sequence or the dimension of the DFT matrix used for constructing the A-ZCZ sequence set. We now propose two extended versions of these methods. The proposed methods can generate a quasi-optimal or optimal polyphase A-ZCZ sequence set where the total number of sequences exceeds the period of the perfect sequence or the dimension of the DFT matrix. In other words, the proposed methods can generate new A-ZCZ sequence sets that cannot be obtained from the known methods.