  We consider three-parameter Yang-Baxter deformations of the $AdS_5\times
T^{1,1}$ superstring for abelian $r$-matrices which are solutions of the
classical Yang-Baxter equation. We find two new backgrounds which are dual to
the dipole deformed Klebanov-Witten gauge theory and to the nonrelativistic
Klebanov-Witten gauge theory with Schr\"odinger symmetry
