Host mixtures are a promising method for agroecological plant disease control. First, we developed an epidemiological model in n dimensions with a large number of resistant host genotypes to explore the effect of host mixtures on the equilibrium prevalence of the disease. A significant amount of resistance genes must be deployed to achieve low disease prevalence, especially if the cost of resistance breaking is low. Also, plant immunity is key to the success of host mixtures against polymorphic pathogen populations. This results from priming-induced cross-protection, whereby plants able to resist infection by specific pathogen genotypes become more resistant to other pathogen genotypes. Strikingly, this phenomenon was thus far absent from mathematical models aiming at designing host mixtures. We previously showed in a simple model of gene-for-gene interaction that priming reduces the prevalence of the disease by the cross-protection process (Clin et al, 2020). We here extend the previous n dimensional model to take priming into account and show that it could help reduce the number of plant genotypes needed to drop the prevalence below an acceptable level. Given the limited availability of resistance genes in cultivars, this mechanism of plant immunity would make the use of host mixtures more realistic.