Before revision:  Here techniques from Karlin (1982) are applied to a multilocus model of mutation with multivariate control over mutation rates, and the reduction principle is found to operate. Constraining assumptions are that mutation distributions follow the transition probabilities of reversible Markov chains, and that all loci are tightly linked. The extension of the reduction principle is shown topologically to require a manifold of mutation rate alterations that are neutral for a new modifier allele , below which will cause a new modifierallele to increase when rare, and above which cause it to go extinct.
After revision:  Here techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is shown topologically to require a manifold of mutation rate alterations that are neutral for a new modifier allele , below which will cause a new modifierallele to increase when rare, and above which cause it to go extinct.