In situ measurements of Arctic clouds frequently show that ice crystal number concentrations (ICNCs) are much higher than the number of available ice-nucleating particles (INPs), suggesting that secondary ice production (SIP) may be active. Here we use a Lagrangian parcel model (LPM) and a large-eddy simulation (LES) to investigate the impact of three SIP mechanisms (rime splintering, breakup from ice-ice collisions and drop shattering) on a summer Arctic stratocumulus case observed during the Aerosol-Cloud Coupling And Climate Interactions in the Arctic (AC-CACIA) campaign. Primary ice alone cannot explain the observed ICNCs, and drop shattering is ineffective in the examined conditions. Only the combination of both rime splintering (RS) and collisional break-up (BR) can explain the observed ICNCs, since both of these mechanisms are weak when activated alone. In contrast to RS, BR is currently not represented in large-scale models; however our results indicate that this may also be a critical ice-multiplication mechanism. In general, low sensitivity of the ICNCs to the assumed INP, to the cloud condensation nuclei (CCN) conditions and also to the choice of BR parameterization is found. Finally, we show that a simplified treatment of SIP, using a LPM constrained by a LES and/or observations, provides a realistic yet computationally efficient way to study SIP effects on clouds. This method can eventually serve as a way to parameterize SIP processes in large-scale models.