Martin,
You can look at patterns between treatments, covariates and responses in various ways. Different methods look for different types of patterns and answer different questions. It's not clear what patterns you're specifically interested in. But, it sounds like you're interested in either what is known as mediation analysis or what is known as moderating variables analysis.
A good introductory book is Jose, P.E. 2013. Doing Statistical Mediation and Moderation. There are others at both introductory and advanced levels.
Best,
Philip Dixon