Which kind of modelling could I perform and are there correction factors to apply to such stable isotope values (C and N) due to the trophic level and/or to the fractionation?
As someone who is heading in this direction for the first time, I am glad you asked.
There is a recent series of responses to a paper published in the Marine Ecology Progress Series (Volumes 472, 490) that provides overviews and critiques of the most popular mixed modeling approaches. My impression is that the standard approaches, such as ISOsource or SIAR modeling, should work as long as you have enough isotopes measured to account for the number of different food sources. It would be worth considering whether you should use deuterium instead of carbon for maximum separation between food sources, but an alternative that uses both C and H isotopes for source separation and N for trophic levels might be even better.