  We derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST
symmetry transformations for any arbitrary D-dimensional St$\ddot
u$ckelberg-modified massive Abelian 3-form theory within the framework of
augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin
(BRST) formalism where, in addition to the horizontality condition (HC), we
exploit the theoretical strength of the gauge invariant restriction (GIR) to
deduce the proper transformations for the gauge, associated (anti-)ghost
fields, auxiliary fields, St$\ddot u$ckelberg compensating field, etc. In fact,
it is an elegant and delicate combination of HC and GIR (within the ambit of
AVSA) that is crucial for all our discussions and derivations. One of the
highlights of our present endeavor is the deduction of a new set of (anti-)BRST
invariant Curci-Ferrari (CF)-type restrictions which are not found in the
massless version of our present theory where only the HC plays an important
role in the derivation of all the (anti-)BRST transformations and a very
specific set of CF-type restrictions. The alternative ways of the derivation of
the full set of the latter, from various theoretical considerations, are also
interesting results of our present investigation.
