We demonstrate the implementation of external cavity optical feedback to improve coherence and promote generation of harmonic states by a mid-infrared quantum cascade laser frequency comb. In particular, we present a Vernier-like scheme to realize harmonic comb states that increase the repetition rate of the comb by a factor of up to 6 and broaden spectral coverages from 46 cm-1 to 92 cm-1. Intermode beatnote and dual comb characterization indicate that the coherence of the comb has greatly improved for sub-optimal devices when the comb is operated in these harmonic states. This approach to control the generation of harmonic states and improve comb performance can be readily incorporated to various sensing systems and has great potential in spectroscopic measurements that require high repetition rates and/or broad optical bandwidth.