We consider a set of variables with a deterministic trend and a stochastic trend. The deterministic trend is allowed to have changes in the intercept and slope. We develop three tests, a cointegration test, a joint test for cointegration and cobreaking, and a joint test for cointegration and cotrending. Our analysis in this paper is complementary to Carrion-i-Silvestre and Kim(2017), which deals with deterministic trends with intercept shifts only.