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Covalent organic frameworks (COFs) are typically designed by breaking down the desired network into feasible building blocks - either simple and highly symmetric, or more convoluted and thus less symmetric. The linkers are chosen complementary to each other such that an extended, fully condensed network structure can form. We show not only an exception, but a design principle that allows breaking free of such design rules. We show that tri- and tetratopic linkers can be combined to form imine-linked [4 + 3] sub-stoichiometric 2D COFs featuring an unexpected bex net topology, and with periodic uncondensed amine functionalities which enhance CO 2 adsorption, can be derivatized in a subsequent reaction, and can also act as organocatalysts. We further extend this class of nets by including a ditopic linker to form [4 + 3 + 2] COFs. The results open up possibilities towards a new class of sub-valent COFs with unique structural, topological and compositional complexities for diverse applications.