  We study non-trivial deformations of the natural action of the Lie algebra
$\mathrm{Vect}({\mathbb R}^n)$ on the space of differential forms on ${\mathbb
R}^n$. We calculate abstractions for integrability of infinitesimal
multi-parameter deformations and determine the commutative associative algebra
corresponding to the miniversal deformation in the sense of \cite{ff}.
