derived smooth geometry
The notion of -plectic form is a generalization of the notion of symplectic form to differential forms of more than two arguments. This is considered in higher symplectic geometry, specifically: in multisymplectic geometry.
This definition has an evident generalization to the case where also is allowed to be a “higher” generalization of a smooth manifold, namely a smooth ∞-groupoid or L-∞ algebroid. See higher symplectic geometry for more on this case.
See the references at multisymplectic geometry.
For instance definition 2.1 in