In this talk, we propose the Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method applied to non-matching muli-patch IgA configurations, that have nested discretizations across interfaces. The IETI-DP method is a domain decomposition algorithm that extends the Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) approach to the isogeometric multi-patch setting. Given that the computational domain is already composed of multiple patches, domain decomposition methods are a natural choice. Initial theoretic insights and analysis of IETI-DP methods were established for conforming Galerkin discretizations with completely matching interfaces in [2] and subsequently for discontinuous Galerkin (dG) discretizations with sliding interfaces in [3]. The analysis is based on the fundamental algebraic framework developed in [1]. In this talk, we present new results on applying IETI-DP to a conforming Galerkin discretization with nested interface spaces. Similarly, this approach yields a Schur complement formulation, which is solved using the conjugate gradient method. We introduce suitable preconditioners for the Schur complement and show appropriate condition number bounds for the preconditioned system in the case of nested interfaces. These estimates are derived within the algebraic framework proposed in [1]. Finally, we provide numerical results for a series of benchmark problems, in which the grid sizes and diffusion parameters vary between patch interfaces and analyze their robustness concerning key parameters such as grid size, spline degree, and diffusion coefficient. These results highlight the applicability and efficiency of the proposed method for addressing more complex non-matching multi-patch configurations.