In the context of effective usage of a scarce spectrum resource, emerging wireless communication standards will demand spectrum sharing with existing systems as well as multiple access with higher spectral efficiency. We mathematically analyze the sum throughput of a spectrum sharing space-division multiple access (SDMA) system, which forms a transmit null in the direction of other coexisting systems while satisfying orthogonal beamforming constraints. For a large number of users N, the SDMA throughput scales as log N at high signal-to-noise ratio (SNR) ((J-1) loglog N at normal SNR), where J is the number of transmit antennas. This indicates that multiplexing gain of the spectrum sharing SDMA is $frac{J-1}{J}$ times less than that of the non-spectrum sharing SDMA only using orthogonal beamforming, whereas no loss in multiuser diversity gain. Although the spectrum sharing SDMA always has lower throughput compared to the non-spectrum sharing SDMA in the non-coexistence scenario, it offers an intriguing opportunity to reuse spectrum already allocated to other coexisting systems.