In this communication, we propose a framework for amalgamating optical-orthogonal frequency-division multiplexing (O-OFDM) and O-OFDM with index modulation (O-OFDM-IM) for optical wireless systems. Both schemes individually have some limitations, e.g., O-OFDM does not provide any granularity for spectral efficiency (SE)/energy efficiency (EE) trade-off, and O-OFDM-IM loses EE for higher order modulation alphabets. By combining O-OFDM and O-OFDM-IM together, the above limitations can be circumvented. Following on from providing the general framework, we use asymmetrically clipped (AC)O-OFDM and ACO-OFDM-IM to demonstrate the validity of the framework. The results presented herein establish that, by consolidating O-OFDM and O-OFDM-IM, in addition to providing SE/EE trade-off, we may realise higher SE and outperform O-OFDM-IM in terms of EE for high SE.