  In this paper we investigate the possible supersymmetric extensions for the
massive (bi)gravity theories in the lowest non-trivial order. For this purpose
we construct the cubic interaction vertices for massive spin-2 and one or two
massive spin-3/2 fields restricting ourselves with the terms containing no more
than one derivative so that such models can be considered as the smooth
deformations for the usual (spontaneously broken) supergravity. Also we
investigate all possible limits where one of the fields becomes massless.
