Mainly I think the way to go about this is to create a single model for all of the data. Using interaction terms should allow you to fit the model you want want and test what you want. But it's always easier to help out when we know something more about the data.
thanks for the suggestions. X is a categorical variable, and C is a continuous variable. I would like to test whether X decreases its effect on Y, when C is added to the model, almost like a Sobel test. I am interested specially in comparing the effects of X on Y across these two models. How would I be able to test whether X increases or decreases its effect on Y when I add an interaction effect? Many thanks.