As an emerging multi-carrier transmission scheme, multiple-mode orthogonal frequency division multiplexing with index modulation (MM-OFDM-IM) conveys information through multiple distinguishable constellations (or modes, alternatively) and their full permutations, increasing the spectral efficiency of OFDM-IM and classical OFDM. However, both MM-OFDM-IM and its extension, that is, MM-OFDM with in-phase/quadrature index modulation (MM-OFDM-IM-IQ), cannot provide any transmit diversity gain, which may be critical for ultra-reliable communications. In this paper, aiming at enhancing the diversity gain of MM-OFDM-IM(-IQ) schemes, coordinate interleaved (CI-)MM-OFDM-IM and linear constellation precoded (LCP-) MM-OFDM-IM-IQ are proposed, both of which achieve a diversity order of two without loss of spectral efficiency. The optimal rotation angle for CI-MM-OFDM-IM and the optimal precoding matrix for LCP-MM-OFDM-IM-IQ, in the sense of maximizing their coding gains, are derived in closed form. Computer simulations corroborate the advantages of the proposed schemes in terms of diversity and bit error rate performance toward next-generation wireless networks.