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An analytic formulation revealing exact contribution of different factors affecting the interference interaction between eigenmodes of a scatterer is presented by utilizing our previously reported modal scattering power formula. For special case of arbitrary multilayer concentric and nonconcentric nanoshells, a recursive method for analytically calculating the T-matrix, and each of these factors is derived. Results for a three layer structure showing the conditions for constructive and destructive interference interactions are discussed in details. It is shown that the interference interaction can occur in the vicinity of the overlapping resonance frequencies of the two spatially overlapping eigenmodes. The role of the phase characteristic of the eigenmodes at the resonance points in the interference phenomena is discussed. Different factors determining the phase behavior originating from either the incidence, or the characteristics of the scatterer itself are studied. These provide the ability to engineer the incidence, and the scatterer properties for achieving desired interference behavior. As a practical example for the application of this approach, reducing radiation loss of a plasmonic nanostructure through tailoring of structural parameters, and synthesis of proper incidence is presented. [ABSTRACT FROM PUBLISHER]