In this paper, we consider the deployment of multiple antennas as a way to exploit spatial diversity in the uplink of multiple access systems that adopt low-density spreading (LDS) with orthogonal frequency-division multiplexing (OFDM). An overloaded LDS-OFDM system is assumed, i. e., the number of users served is assumed greater than the number of resources. A basic model is developed and from it we design multiplexing spreading signatures based on space-frequency block codes (SFBC) to enhance the system's error performance. Computer simulations results reveal that the proposed multipleinput multiple-output (MIMO) LDS-OFDM scheme achieves full spatial diversity gain regardless the level of fading correlation between neighboring subcarriers. In contrast, a standard LDS scheme is shown to achieve full spatial diversity gain only under perfectly uncorrelated frequency fading, which favors the proposed scheme. Moreover, the spatial diversity benefits of MIMO LDS-OFDM comes with no additional complexity, as an iterative message-passing algorithm with the same complexity for both the proposed and the standard schemes approaches the respective optimal performances with only 2 iterations. These features make the proposed MIMO LDS-OFDM scheme a strong candidate for future wireless networks.