Generalized Global Symmetries of D-dimensional Quantum Field Theories (QFTs) can be interpreted in terms of (D+1)-dimensional bulk Symmetry Theory (SymTh), which often turns out to be a gapped Symmetry Topological Field Theory (SymTFT). In this setting interacting degrees of freedom arise as edge modes of a higher-dimensional bulk system. We further show that the combined (D + 1)-dimensional bulk and D-dimensional edge mode theory can serve as the edge modes of a (D+2)-dimensional bulk theory, which leads to a nested structure of SymThs. We show how this structure naturally arises in a number of string-based constructions of QFTs with both discrete and continuous symmetries.