Can one have two different sources for postdoc fundings together in Europe? Let's consider the hypothetical situation of a postdoctoral candidate C, who get funded simultaneously as follows, starting at the same or different times, with overlap:


Funding agencies F_1, F_2 (for example, Marie Curie, FWO, Danish Research Council...), where for each F_i, he wrote a proposal with a research team or host H_i, who did not have any funding on their own, but agreed to supervise C.
Department D (for example, University of Pennsylvania), who offered candidate C a postdoc from their own funding directly.


Can C earn from both the fundings in case of 1. and 2.? or; it depends on the funding agencies rules? 

I went though the rules of some Marie Curie postdoc fellowships, I don't think I noticed any rules that states anything against having two fundings together?
The main issue I can think of would be time allotment. Most grants require you to specify how what percentage of your time you will spend on the grant. As you cannot overcommit yourself (i.e., total time allotment cannot exceed 100%), you'll have to specify that in the proposal. Many professors have funding from multiple grants at any given time, so this situation is not too unusual.

Do note, though, that it is highly likely that once "Department D" catches on that you have an external source of funding, they may decide to withdraw their offer and provide the funding to someone who has none. Not sure how that would work.