In this paper, we propose a composite multiplemode orthogonal frequency division multiplexing with index modulation (C-MM-OFDM-IM) scheme to increase the spectral efficiency (SE) of OFDM-IM systems by extending the indexing to the energy and constellation domains. In C-MM-OFDM-IM, the information bits are mapped to not only the subcarrier activation patterns (SAPs) and modulation symbols, but also the energy allocation patterns (EAPs) and constellation activation patterns (CAPs). To cope with the practical situations, we propose a variant IM scheme named C-MM-OFDM-IM-II to build a new mapping rule between information bits and the increased CAPs, capable of further increasing the SE of C-MM-OFDM-IM. Upper-bounded bit error rate (BER) and lower-bounded achievable rate are both derived in closed-form to evaluate the performance of C-MM-OFDM-IM(-II). Moreover, we further propose two enhanced schemes, named generalized C-MM-OFDM-IM(-II) and C-MM-OFDM with in-phase/quadrature IM(-II), where the former jointly considers all SAPs, EAPs, CAPs and modulated symbols, while the latter expands the index implementation to the in-phase and quadrature constellation domains. Simulation results show that C-MM-OFDM-IM(-II) outperforms the conventional OFDM-IM related schemes, especially in the high signalto-noise ratio (SNR) region, and verify the accuracy of the theoretical analysis for the upper-bounded BER and achievable rate.