In our recent work we applied the multiple overlapping autoionizing resonance formalism of Davis and Feldkamp to electron-cadmium ionization. We also extended their formalism to include the scattered electron's angular dependence in order to calculate the triple-differential cross section. In this paper we generalize our formalism in order to apply it to any process involving overlapping resonances. We show that the effect of the interaction between different resonances can be treated as a correction factor to the isolated resonance treatment of the problem. We have applied our approach to four physically significant cases, each consisting of two overlapping resonances. Our results indicate that even in the case where the resonances are only somewhat overlapping, the correction factor makes a considerable contribution. In the case where one of the resonances is very close to the other one, the deviation from the isolated resonance treatment is significant.