In this study, we propose designs of an interband cascade laser (ICL) active region able to emit in the application-relevant mid infrared (MIR) spectral range and to be grown on an InP substrate. This is a long-sought solution as it promises a combination of ICL advantages with mature and cost-effective epitaxial technology of fabricating materials and devices with high structural and optical quality, when compared to standard approaches of growing ICLs on GaSb or InAs substrates. Therefore, we theoretically investigate a family of type II, “W”-shaped quantum wells made of InGaAs/InAs/GaAsSb with different barriers, for a range of compositions assuring the strain levels acceptable from the growth point of view. The calculated band structure within the 8-band k·p approximation showed that the inclusion of a thin InAs layer into such a type II system brings a useful additional tuning knob to tailor the electronic confined states, optical transitions’ energy and their intensity. Eventually, it allows achieving the emission wavelengths from below 3 to at least 4.6 μm, while still keeping reasonably high gain when compared to the state-of-the-art ICLs. We demonstrate a good tunability of both the emission wavelength and the optical transitions’ oscillator strength, which are competitive with other approaches in the MIR. This is an original solution which has not been demonstrated so far experimentally. Such InP-based interband cascade lasers are of crucial application importance, particularly for the optical gas sensing.