This work investigates spatial-mode multiplexing (SMM) for practical free-space optical communication (FSO) systems using direct detection. Unlike several works in the literature where mutually incoherent channels are assumed, we consider mutually coherent channels that accurately describe SMM FSO systems employing a single laser source at the transmitter with a narrow linewidth. We develop an analytical model for such mutually coherent channels and derive expressions for aggregate achievable rate (AAR). Through numerical simulations, it was shown that there exist optimal transmit mode sets which result in the maximal asymptotic AAR at high transmitted power. Moreover, in order to resolve the reliability issues of such SMM FSO systems in the presence of turbulence, a so-called mode diversity scheme is proposed that can be easily implemented along with SMM FSO systems. It is demonstrated that mode diversity can significantly improve the outage probability and the outage achievable rate performance of the multiplexed channels in SMM FSO systems degraded by turbulence.