Persistent outflow of supercooled Ice Shelf Water (ISW) from beneath McMurdo Ice Shelf creates a sub-ice platelet layer (SIPL) having a unique crystallographic structure under the sea ice in McMurdo Sound (MMS), Antarctica. A new frazil-ice-laden ISW plume model that encapsulates the combined nonlinear effects of the vertical distributions of supercooling and frazil ice concentration (FIC) on frazil ice growth is applied to MMS, and is shown to reproduce the observed ISW supercooling and SIPL distributions. Using this model, the dependence of SIPL thickening rate on ISW supercooling in MMS is investigated. Results are found to be sensitive to the choice of frazil ice suspension index, which determines the vertical distribution of FIC. For each suspension index, SIPL thickening rate can be expressed as an exponential function of ISW supercooling. The complex dependence on FIC highlights the need to improve frazil ice observations within the ice-ocean boundary layer.