  In article is constructed a wide couple of pairwice non-isomorphic separable
superreflexive Banach spaces E that are subspace homogeneous. Their conjugates
are quotient homogeneous. None of this couple neither isomorphic to its
Cartesian square nor has the approximation property. At the same time, any such
E is isomorphic to E+ E+ W for some Banach space W and, hence, solves the
Schroeder - Bernstein problem.
