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The ergodic capacity region of a multiple access separately-correlated Rician fading MIMO channel is investigated by using an asymptotic approach. It is assumed that the number of transmit and receive antennas grow asymptotically approaching finite values while the number of users and the SNR are kept finite. It is shown by numerical results that this asymptotic approach is very accurate even when the number of antennas is as low as a few units. The ergodic capacity achieving covariance matrices for all users are derived according to the algorithm provided and the corresponding capacity is compared with the mutual information achieved by iid power allocation. Monte-Carlo simulations are also reported in order to verify the accuracy of the asymptotic results.