The dynamic behavior of nearly periodic structures with 2D or 3D substructures subject to geometric changes is addressed. These geometric changes can represent any classic parametric variations (thicknesses) or mesh changes where shape functions and mesh parameters are used to move the nodes of a baseline substructure. Reduced order models of substructures can be obtained using the Craig-Bampton (CB) method. The issue with this method is the requirement that the component modes as well as the reduced matrices of the substructures be computed many times for different substructures, when parametric changes come into play. To solve this issue and quickly recompute the reduced substructure matrices, they can be interpolated over a parametric space. This means (i) expressing the reduced matrices at interpolation points (e.g., some distorted FE meshes) and (ii) interpolating the reduced matrices between the interpolation points. To improve the efficiency of the interpolation strategy, an interface reduction (between the substructures) for modeling a nearly periodic structure can be considered where the projection basis consists of the interface modes of the equivalent purely periodic structure. Although efficient, the aforementioned interpolation strategy is prone to lack of accuracy at high frequencies. First, to express the reduced substructure matrices in compatible coordinate systems, only a few low-order fixed interface modes must be kept in the CB basis. Next the proposed interface reduction considers the interface modes of a purely periodic structure, which as such cannot account for geometric modifications. To improve the accuracy of the interpolation strategy, two basis enrichment techniques can be proposed as follows: (1) Enrichment of the CB basis of the substructures with high-order static modes. Prior to any matrix interpolation, these modes are orthogonalized and transformed using a correlation criterion. Then, a reduced set of these high-order static modes are used to enrich the CB basis at the interpolation points. (2) Enrichment of the basis of interface modes with static correction vectors. The strategy consists in adding to the interface modes a set of static response vectors that result from parametric changes, i.e., those induced by the perturbations of the stiffness matrices of the substructures.