  In this paper, we consider representations of $p$-adic classical groups
parabolically induced from the products of shifted Speh representations and
unitary representations of Arthur type of good parity. We describe how to
compute the socles (the maximal semisimple subrepresentations) of these
representations. As a consequence, we can determine whether these
representations are reducible or not. In particular, our results produce many
unitary representations, which are called complementary series.
