As an improved variant of a previously published subcarrier index-power modulated optical orthogonal frequency division multiplexing (SIPM-OOFDM), a signal transmission technique termed SIPM-OOFDM with subcarrier grouping (SIPM-SG-OOFDM) is proposed and investigated for the first time. In SIPM-SG-OOFDM, each symbol is divided into multiple subcarrier groups, each of which is assigned with a specific power pattern according to an incoming data sequence. As such, in comparison with conventional OOFDM, extra information bits are conveyed without significantly compromising the transceiver complexity. In addition, subcarrier grouping also offers highly desired zero-overhead automatic error correction at the receiver. Detailed analysis and numerical simulations are undertaken to identify optimum SIPM-SG-OOFDM transceiver parameters and also to explore the corresponding maximum achievable transmission performances over passive optical network systems based on intensity modulation and direct-detection. It is shown that, compared to SIPM-OOFDM, SIPM-SG-OOFDM not only increases the signal transmission capacity by 11%, but also improves the system power budget by approximately 1.0 dB.