Trying to perform non-parametric change point tests for multivariate data using empirical processes is much more difficult that in the univariate case, since the limiting distribution depends on the unknown joint distribution function or its associated copula. In order to solve this problem, we extend the multiplier central limit theorem to empirical processes of pseudo-observations to build asymptotically independent copies of these processes. Examples of applications to change point problems for i.i.d observations and innovations of dynamic models are given, both for the full distribution and the associated copula.