  We obtain existence and multiplicity results for the solutions of a class of
coupled semilinear bi-harmonic Schr\"{o}dinger equations. Actually, using the
classical Mountain Pass Theorem and minimization techniques, we prove the
existence of critical points of the associated functional constrained on the
\emph{Nehari manifold}.
  Furthermore, we show that using the so-called \emph{fibering method} and the
\emph{Lusternik-Schnirel'man theory} there exist infinitely many solutions,
actually a countable family of critical points, for such a semiliner bi-hamonic
Schr\"{o}dinger system under study in this work.
