The effect of relative Mn and hole concentrations on ferromagnetic order in thin (Ga,Mn)As films is investigated in using modulation doped (Al,Ga,Be)As/(Ga,Mn)As heterostructures grown by molecular beam epitaxy. Our Hall effect measurements indicate that the hole concentration p in the (Ga,Mn)As layers increases with the amount of Be in the (Al,Ga,Be)As barrier. At low Be amount in the barrier, the Curie temperature TC of the (Ga,Mn)As layer is enhanced compared to that observed without Be doping. However, as the Be content in the (Al,Ga,Be)As barrier is increased further, this trend is reversed: TC is observed to decrease, and eventually the ferromagnetic order in (Ga,Mn)As disappears altogether, as seen in magnetization measurements. This behavior is in disagreement with the mean field Zener model of magnetic semiconductors, since that model predicts TC to be simply proportional to p1/3. Our results suggest that this model fails at very high values of p, especially when p exceeds the Mn concentration in (Ga,Mn)As.