After the vision and the overall objectives of future wireless networks for 2020 and beyond have been defined, standardization activities for fifth generation (5G) wireless networks have been started. Although it is expected that 5G new radio (NR) will be based on cyclicly prefixed orthogonal frequency division multiplexing (CP-OFDM)-based waveforms along with multiple waveform numerologies, the sufficiency of CP-OFDM-based NR is quite disputable due to the continuing massive growth trend in number of wireless devices and applications. Therefore, studies on novel radio access technologies (RATs) including advanced waveforms and more fiexible radio accessing schemes must continue for future wireless networks. Generalized frequency division multiplexing (GFDM) is one of the prominent non-CP-OFDM-based waveforms. It has recently attracted significant attention in research because of its beneficial properties to fulfill the requirements of future wireless networks. Multiple-input multiple-output (MIMO)-friendliness is a key ability for a physical layer scheme to satisfactorily match the foreseen requirements of future wireless networks. On the other hand, the index modulation (IM) concept, which relies on conveying additional information bits through indices of certain transmit entities, is an emerging technique to provide better spectral and energy efficiency. In this paper, considering the advantages of non-CP-OFDM-based waveforms and the IM concept, we present a framework, which integrates GFDM with space and frequency IM schemes to provide flexible and advanced novel RATs for future wireless networks. Several MIMO-GFDM schemes are provided through the proposed framework and their bit error ratio performances, computational complexities, and spectral efficiencies are analyzed. Based on the obtained results, a guideline for selecting the proper MIMO-GFDM scheme considering target performance criterion is given. It has been demonstrated that the proposed framework has a strong potential to engineer the space-frequency structure according to channel conditions and use cases, and it provides a great flexibility that can be easily tuned to address the required performance criterion.