Evolution of resistance is a major barrier to successful deployment of gene-drive systems to suppress natural populations, which could greatly reduce the burden of many vector-borne diseases. Multiplexed guide RNAs (gRNAs) that require resistance mutations in all target cut sites are a promising antiresistance strategy since, in principle, resistance would only arise in unrealistically large populations. Using stochastic simulations that accurately model evolution at very large population sizes, we explore the probability of resistance due to three important mechanisms: 1) nonhomologous end-joining mutations, 2) single-nucleotide mutants arising de novo, or 3) single-nucleotide polymorphisms preexisting as standing variation. Our results explore the relative importance of these mechanisms and highlight a complexity of the mutation–selection–drift balance between haplotypes with complete resistance and those with an incomplete number of resistant alleles. We find that this leads to a phenomenon where weakly deleterious naturally occurring variants greatly amplify the probability of multisite resistance compared to de novo mutation. This key result provides design criterion for antiresistance multiplexed systems, which, in general, will need a larger number of gRNAs compared to de novo expectations. This theory may have wider application to the evolution of resistance or evolutionary rescue when multiple changes are required before selection can act.