In this paper, we study the uplink channel throughput performance of a proposed novel multiple-antenna hybrid-domain non-orthogonal multiple access (MA-HD-NOMA) scheme. This scheme combines the conventional sparse code multiple access (SCMA) and power-domain NOMA (PD-NOMA) schemes in order to increase the number of users served as compared to conventional NOMA schemes and uses multiple antennas at the base station. To this end, a joint resource allocation problem for the MA-HD-NOMA scheme is formulated that maximizes the sum rate of the entire system. For a comprehensive comparison, the joint resource allocation problems for the multi-antenna SCMA (MA-SCMA) and multi-antenna PD-NOMA (MA-PD-NOMA) schemes with the same overloading factor are formulated as well. Each of the formulated problems is a mixed-integer non-convex program, and hence, we apply successive convex approximation (SCA)- and reweighted $\ell_1$ minimization-based approaches to obtain rapidly converging solutions. Numerical results reveal that the proposed MA-HD-NOMA scheme has superior performance compared to MA-SCMA and MA-PD-NOMA.