We propose a mode demultiplexing hybrid (MDH) that integrates mode demultiplexing, local oscillator power splitting, and optical 90-deg mixing using multi-plane light conversion (MPLC). We demonstrate the realization of a three-mode MDH using four phase plates, one more than what is required for an MPLC-based mode demultiplexer, via numerical simulations. The performance of the three-mode MDH is comparable to that of commercial single-mode 90-deg hybrids. This multiple-functionality device enables simplification of the coherent optical front end of mode-division multiplexing receivers.