We give a necessary and sufficient condition for the existence of an increasing coupling of N ($N\geq 2$) synchronous dynamics on $S^{\mathbb Z^d}$ (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered, applications to attractive PCA's are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.