To address the uplink transmit power minimization problem for multi-cell scenarios， this paper proposes an uplink transmission scheme for the coordinated multiple point-nonorthogonal multiple access （CoMP-NOMA） system with the collaboration of multiple intelligent reflecting surfaces （IRSs）. Specifically， a couple of IRSs are deployed at the cell-center and the cell-edge respectively， to improve the transmission quality for both the cell-center and the cell-edge users， in which the inter-IRS reflection between the cell-center and the cell-edge IRSs is considered. To solve the formulated power minimization problem， the relation between the power allocation coefficients and the phase shifts is developed. Further， the joint optimization problem of power allocation and phase shift is converted into a pure phase shift determination problem， which is transformed to a series of one-dimensional search problems by using the sequential rotation method. Simulation results demonstrate that the proposed solution significantly outperforms other benchmark schemes in terms of transmit power consumption under the same simulation setups.