We present a comparative study of high carrier density transport in mono-, bi-, and trilayer graphene using electric double-layer transistors to continuously tune the carrier density up to values exceeding 1014 cm-2. Whereas in monolayer the conductivity saturates, in bi- and trilayer filling of the higher-energy bands is observed to cause a nonmonotonic behavior of the conductivity and a large increase in the quantum capacitance. These systematic trends not only show how the intrinsic high-density transport properties of graphene can be accessed by field effect, but also demonstrate the robustness of ion-gated graphene, which is crucial for possible future applications.