Disparities between the measured concentrations of ice-nucleating particles (INPs) and in-cloud ice crystal number concentrations (ICNCs) have led to the hypothesis that mechanisms other than primary nucleation form ice in the atmosphere. Here, we model three of these secondary production mechanisms - rime splintering, frozen droplet shattering, and ice–ice collisional breakup – with a six-hydrometeor-class parcel model. We perform three sets of simulations to understand temporal evolution of ice hydrometeor number (Nice), thermodynamic limitations, and the impact of parametric uncertainty when secondary production is active. Output is assessed in terms of the number of primarily nucleated ice crystals that must exist before secondary production initiates (NINP(lim)) as well as the ICNC enhancement from secondary production and the timing of a 100-fold enhancement. Nice evolution can be understood in terms of collision-based nonlinearity and the "phasedness" of the process, i.e., whether it involves ice hydrometeors, liquid ones, or both. Ice–ice collisional breakup is the only process for which a meaningful NINP(lim) exis ... mehrts (0.002 up to 0.15 L−1). For droplet shattering and rime splintering, a warm enough cloud base temperature and modest updraft are the more important criteria for initiation. The low values of NINP(lim) here suggest that, under appropriate thermodynamic conditions for secondary ice production, perturbations in cloud concentration nuclei concentrations are more influential in mixed-phase partitioning than those in INP concentrations.