  We consider smooth deformations of the $CR$ structure of a smooth
$2$-pseudoconcave compact $CR$ submanifold $\textsf{M}$ of a reduced complex
analytic variety $\textsf{X}$ outside the intersection $D\,{\cap}\,\textsf{M}$
with the support $D$ of a Cartier divisor of a positive line bundle
$\texttt{F}_{\textsf{X}}.$ We show that nearby structures still admit
projective $CR$ embeddings. Special results are obtained under the additional
assumptions that $\textsf{X}$ is a projective space or a Fano variety.
