  We introduce higher strip deformations, which give a way of constructing
affine deformations of discrete free groups in the image of the irreducible
representation $\operatorname{PSL}_2\mathbb{R}\to \operatorname{SO}(2n,2n-1)$.
We use the Margulis invariant to find a properness condition for these
deformations, showing that each convex cocompact free group admits affine
deformations acting properly on $\mathbb{R}^{4n-1}$. Using our method we can
also construct proper affine actions of virtually free groups, which we
demonstrate by finding proper actions of $C_2 \star C_3$ on $\mathbb{R}^7.$
