The global symmetries of a -dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a (+1)-dimensional symmetry topological field theory (SymTFT). In this work we construct a (+1)-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large averaging where the topological sectors of different large replicas become dressed by additional extended operators associated with the SymTree.