Using two-dimensional THz spectroscopy in combination with numerical models, we investigate the dynamics linked to carrier multiplication caused by high-field THz excitation of the low-gap semiconductor InSb. In addition to previously reported dynamics connected with quasiballistic carrier dynamics, we observe other spectral and temporal features that we attribute to impact ionization for peak fields above 60 kV/cm, which continue up to the maximum investigated peak field of 430 kV/cm. At the highest fields we estimate a carrier multiplication factor greater than 10 due to impact ionization, which is well-reproduced by a numerical simulation of the impact ionization process which we have developed.