Compare the results of two canonical correlation analyses (CCA)

I have four datasets: morphological measurements for a set of species (M1), ecological measurements for the same set of species (E1), morphological measurements for a second set of species (M2), and ecological measurements for this second set of species (E2).

I am interested in finding the linear combinations of variables between M1 and E1, and between M2 and E2. That is, I’d like to know what combinations of morphological measurements are associated with what combination of ecological measurements–for each set of species separately. This seems like a good use of CCA (two separate CCAs).

But here’s where things get tricky for me. I’d like to see whether the same linear combinations from one set of species do a good job of explaining the variation in the second set of matrices. And I’d like to see how they differ, if possible…e.g. variable 3 from M2 would be more heavily loaded on a given axis if we didn’t constrain the second CCA by the linear combinations found from the first.

Is this making any sense? I’m not a statistician, so I admit my lack of experience up front. I could see simply running these as two separate CCAs, then comparing the results qualitatively. But that doesn’t seem very rigorous. Should I be considering some other approach entirely?

Thanks for any input.