Aircraft jet engines operating at high altitudes in ice crystal clouds can experience operational problems and/or damage resulting from accretion of ingested ice crystals within the compressor. It is believed the ice crystals partially melt, allowing them to stick to internal components. A method for modelling such mixed-phase accretion is required to de-risk new engine designs, modify existing designs with such icing issues and define critical operating points for scrutiny in proposed ice crystal certification tests. This paper presents preliminary results for a modelling approach which treats the accretion process as strictly a sticking phenomenon, ignoring heat transfer, phase change, runback and other location-dependent effects commonly used in the analysis of supercooled water icing. Ice-on-ice growth is described by a sticking efficiency, defined as the fraction of the mixed-phase impinging mass flux which remains on the surface (i.e. sticks). Experimental results are presented for 3 test articles tested in a small mixed-phase icing tunnel located in an altitude chamber (Research Altitude Test Facility or RATFac) at the National Research Council of Canada. These results show that the sticking efficiency is highly correlated with the ratio of liquid water content (LWC) to total water content (TWC) in the freestream, reaching a maximum value of 0.4-0.5 at melt (LWC/TWC) ratios in the approximate range 10-20%, as measured with a multi-element probe. It is shown that sticking efficiencies are largely independent of TWC, Mach number (M) and particle size at normal incidence (i.e. at the stagnation point) at these melt ratios, at least in the limited ranges of these variables investigated, but are strongly dependent on these parameters at oblique impingement angles. It is also shown that accretions can grow to a very large size at an almost constant rate at high levels of TWC. The experimental results are used to develop an erosion-based semi-empirical accretion model which at least partially explains this super-growth phenomenon and predicts most of the experimental results with acceptable fidelity. The model predicts that the almost unlimited growth observed in the experiments is possible at lower Mach numbers (e.g. 0.25) for TWC levels exceeding ~10g/m3, when the sticking efficiency remains finite at all particle impingement angles. The model also predicts that such growth is unlikely for higher Mach numbers (e.g. 0.4), at least for the 45μ (MVD) particles to which the model is applied. Smaller particles will likely extend the Mach number range over which the sticking efficiency remains finite.