  We study completely contractive representations of product systems of
$C^*$-correspondences over semigroups. For a product system of
$C^*$-correspondences over the semigroup $\mathbb{N}^2$, we prove that every
such representation can be dilated to an isometric (or Toeplitz)
representation. We use it to prove that every pair of commuting CP maps on a
von Neumann algebra $M$ can be dilated to a commuting pair of endomorphisms (on
a larger von Neumann algebra).
