Tests for the cointegrating rank of a vector autoregressive process are considered which allow for possible exogenous shifts in the mean of the data generation process. The break points are assumed to be known a priori. It is proposed to estimate and remove the deterministic terms such as mean, linear trend term and a shift in a first step. Then systems cointegration tests are applied to the adjusted series. The resulting tests are shown to have known limiting null distributions which are free of nuisance parameters and do not depend on the break point. The tests are applied for analyzing the number of cointegrating relations in a German money demand system.