The downlink of a coordinated multi-cell distributed antenna system is considered. In , coordinated port selection was shown to achieve significant performance gains. However, in the system considered therein, the ports in each cell were constrained to transmit only to user terminals (UTs) in that cell. In this work, we consider a generalization of the problem considered in  by alleviating this constraint. We formulate the problem of determining the ports that maximize the minimum signal to interference plus noise ratio observed by the UTs as a binary-constrained optimization problem. Observing that it is NP-hard, we propose a semidefinite relaxation and Gaussian randomization based technique to obtain close-to-optimal solutions. Our simulation results show that the performance achieved by the proposed technique approaches that of the optimal solution. It is also shown that the proposed technique outperforms the one in , particularly for cell-edge UTs, albeit with an increased computational complexity.