  We present a theoretical study of (Ga,Mn)(As,C) diluted magnetic
semiconductors with high C acceptor density that combines insights from
phenomenological model and microscopic approaches. A tight-binding coherent
potential approximation is used to describe the electronic structure in the
presence of Mn$_{\rm Ga}$ and C$_{\rm As}$ impurities. We find only a small
effect of C on the distribution and coherence of electronic states close to the
top of the valence band and on the coupling between Mn moments, even at doping
levels of several per cent. These results justify applying the model of
ferromagnetic Mn-Mn coupling mediated by itinerant holes in the valence band
also to C doped samples. The increase of ferromagnetic transition temperature
due to the presence of C acceptors is illustrated by calculations that use the
k.p Kohn-Luttinger description of the GaAs valence band and assume systems
where Mn local moment and itinerant hole densities can be varied independently.
