Orthogonal frequency division multiplexing with index modulation (OFDM-IM) performs transmission by considering two modes over OFDM subcarriers, which are the null and the conventional M-ary signal constellation. The spectral efficiency (SE) of the system, however, is limited, since the null mode itself does not carry any information and the number of subcarrier activation patterns increases combinatorially. In this paper, a novel IM scheme, called multiple-mode OFDM-IM (MM-OFDM-IM), is proposed for OFDM systems to improve the SE by conveying information through multiple distinguishable modes and their full permutations. A practical and efficient mode selection strategy, which is constrained on the phase shift keying/quadrature amplitude modulation constellations, is designed. Two efficient detectors that provide different tradeoffs between the error performance and detection complexity are also proposed. The principle of MM-OFDM-IM is further extended to the in-phase and quadrature components of OFDM signals, and the method of generating multiple modes from the M-ary pulse amplitude modulation constellation for this modified scheme is also introduced. Bit error rate (BER) analyses are provided for the proposed schemes. Monte Carlo simulations on BER corroborate the analyses and show that the proposed schemes appear as promising multi-carrier transmission alternatives by outperforming the existing OFDM-IM counterparts.