Can one have two different sources for postdoc fundings together in Europe?
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.