In-cloud measurements of ice crystal number concentration can be orders of magnitude higher than the precloud ice nucleating particle number concentration. This disparity may be explained with secondary ice production processes. Several such processes have been proposed, but their relative importance and even the exact physics are not well known. In this work, a six-hydrometeor-class parcel model is developed to investigate the ice crystal number enhancement, both its bounds and its value for different cloud states, from rime splintering and breakup upon graupel-graupel collision. The model also includes ice aggregation and droplet coalescence, ice hydrometeor nonsphericity, and a time delay formulation for hydrometeor growth. Conditions to maximize the breakup contribution, as well as the effects of nonsphericity and turbulence, are discussed. We find that the largest enhancement of ice crystal number occurs for “intermediate” conditions, characterized by moderate updrafts and activation and nucleation rates. In this case, vertical motion is strong enough, and new hydrometeor formation limited enough, to sustain supersaturation as hydrometeors grow to larger sizes. After these larger hydrometeors form at sufficient number concentrations, the ice crystal number can be enhanced by a factor of 104 in some cases relative to the number generated by primary ice nucleation alone. Excluding ice hydrometeor nonsphericity limits secondary production significantly, and the parcel updraft can modulate it by about an order of magnitude. ©2017. American Geophysical Union. All Rights Reserved.