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This paper proposes a generic analysis framework for a grid supporting modular multilevel converter (MMC)-high voltage DC (HVDC) in a multi-infeed of line commutated converter (LCC) and MMC (MILM) system. MMC-HVDC can support the grid by compensating for the exact reactive power consumptions within the MMC-HVDC system and the varying power system conditions in the MILM system. Maximum active/reactive power capability (MPQC) curve and PQ loading curve comparison process is introduced to properly design a grid supporting MMC-HVDC. While the MPQC curve presents the maximum PQ range of the MMC-HVDC system based on the submodule capacitance value and the modulation index, the PQ loading curve presents the reactive power requirement from the power system that MMC-HVDC needs to compensate. Finally, the comparison of these two curves yields the proper value of submodule capacitance and the modulation index for sufficiently supporting the MILM system. The proposed framework is validated with detailed PSCAD/EMTDC simulation; it demonstrated that it could be applied to various power system conditions.