We extend the methodology for calculating Auger recombination from first principles to include spin-orbit interaction, which allows us to study materials in which the spin-orbit splitting and the band gap are of similar magnitude. We use this methodology to compute the direct and indirect Auger coefficients in InAs and related alloys. The direct process involves only Coulomb interaction, while the indirect process is mediated by phonons. We show how the spin-orbit split-off states allow for efficient direct Auger recombination, greatly enhancing the excitation rate of Auger holes due to a near resonance between the spin-orbit splitting and the band gap of the material. We find that the direct hole-hole-electron Auger recombination coefficient decays exponentially with increasing band gap, while the electron-electron-hole Auger recombination coefficient decays faster than exponentially. Additionally, we modeled the phonon-assisted process in InAs and show that the direct Auger process is dominant.