  Continuing our exploration of maximally supersymmetric gauge theories (MSYM)
deformed by higher dimensional operators, in this paper we consider an
off-shell approach based on pure spinor superspace and focus on constructing
supersymmetric deformations beyond the first order. In particular, we give a
construction of the Batalin-Vilkovisky action of an all-order non-Abelian
Born-Infeld deformation of MSYM in the non-minimal pure spinor formalism. We
also discuss subtleties in the integration over the pure spinor superspace and
the relevance of Berkovits-Nekrasov regularization.
