Photoreflectance spectroscopy has been used to study the energy gap and spin-orbit splitting in InNAsSb alloys containing different amounts of nitrogen and antimony. It has been observed that nitrogen mainly affects the conduction band, without having any influence on the spin-orbit splitting, whereas antimony significantly modifies the spin-orbit splitting. The N- and Sb-related modifications to the band structure lead to alloys which have a spin orbit splitting larger than the energy gap. Consequently, InNAsSb alloys are very promising for use in optoelectronic devices since they offer a route towards the reduction of non-radiative Auger recombination.