In-situ measurements of Arctic clouds frequently show that ice crystal number concentrations (ICNCs) are much higher than the available ice-nucleating particles (INPs), suggesting that Secondary Ice Production (SIP) may be active. Here we use a Lagrangian Parcel Model and a Large Eddy Simulation to investigate the impact of three SIP mechanisms (rime-splintering, break-up from ice-ice 20 collisions and droplet-shattering) on a summer Arctic stratocumulus case observed during the Cloud Coupling And Climate Interactions in the Arctic (ACCACIA) campaign. Primary ice alone cannot explain the observed ICNCs, and droplet-shattering is an ineffective SIP mechanism for the conditions considered. Rime-splintering, a mechanism that usually dominates within the studied temperature range, is also weak owing to the lack of large droplets to initiate this process. In contrast, break-up enhances 25ICNCs by 1-1.5 orders of magnitude, bringing simulations in good agreement with observations.Combining both processes can further explain some of the largest ICNCs observed. The main conclusions of this study show low sensitivity to the assumed INP and Cloud Condensation Nuclei (CCN) conditions. Our results indicate that collisional break-up may be an important ice-multiplication mechanism that is currently not represented in large-scale models. Finally, we also show that a 30 simplified treatment of SIP, using a LPM constrained by a LES and/or observations, provides a realistic yet computationally efficient description of SIP effects that can eventually serve as an efficient way to parameterize this process in large-scale models.