  We construct a continuum of mutually non-isomorphic separable Banach spaces
which are complemented in each other. Consequently, the Schroeder-Bernstein
Index of any of these spaces is $2^{\aleph_0}$. Our construction is based on a
Banach space introduced by W. T. Gowers and B. Maurey in 1997. We also use
classical descriptive set theory methods, as in some work of V. Ferenczi and C.
Rosendal, to improve some results of P. G. Casazza and of N. J. Kalton on the
Schroeder-Bernstein Property for spaces with an unconditional
finite-dimensional Schauder decomposition.
