We consider a recently-proposed model which posits the existence of composite dark matter , wherein dark “ quarks ” transforming as fundamentals under an SU ( 3 ) _ { d } gauge group undergo a confining phase and form dark baryons . The model attempts to explain both the \mathcal { O } ( 1 ) relic density ratio , \Omega _ { \mathrm { dark } } / \Omega _ { \mathrm { baryon } } \sim 5.4 , as well as the asymmetric production of both dark and baryonic matter via leptogenesis . Though the solution of \beta functions for SU ( 3 ) _ { c } and SU ( 3 ) _ { d } constitutes the main drive of the model , no threshold corrections were taken into account as the renormalization scale crosses the mass threshold of the heavy new fields in the model . We extend this work by explicitly calculating the threshold-corrected renormalization-group flow for the theory using an effective-field matching technique . We find that the theory has a much wider range of applicability than previously thought , and that a significant fraction of models ( defined by the number of fields contained therein ) is able to account for the observed relic density .