We construct higher categories of iterated spans, possibly equipped with extra structure in the form of higher-categorical local systems, and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum field theories, which are the framed versions of the classical topological quantum field theories considered in the quantization programme of Freed–Hopkins–Lurie–Teleman. Using this machinery, we also construct an (Formula presented.)-category of symplectic derived algebraic stacks and Lagrangian correspondences and show that all its objects are dualizable.