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We study supergeometric structures underlying frame-like Lagrangians. We showthat for the theory in n spacetime dimensions both the frame-like Lagrangianand its gauge symmetries are encoded in the target supermanifold equipped withthe odd vector field, the closed 2-form of ghost degree n-1, and the scalarpotential of ghost degree n. These structures satisfy a set of compatibilityconditions ensuring the gauge invariance of the theory. The Lagrangian and thegauge symmetries have the same structures as those of AKSZ sigma model so thatframe-like formulation can be seen as its presymplectic generalization. Incontrast to the conventional AKSZ model the generalization allows to describesystems with local degrees of freedom in terms of finite-dimensional targetspace. We argue that the proposed frame-like approach is directly related deDonder-Weyl polymomentum Hamiltonian formalism. Along with the standardfield-theoretical examples like Einstein-Yang-Mills theory we consider freehigher spin fields, multi-frame gravity, and parameterized systems. Inparticular, we propose the frame-like action for free totally symmetricmassless fields that involves all higher spin connections on an equal footing.

Frame-like Lagrangians and presymplectic AKSZ-type sigma models