Graphene grown on the (0001) basal plane of silicon carbide, i.e. on the SiC(0001) surface, is an extremely promising candidate for future nano-electronic applica-tions. However, hurdles such as strong electron doping and low carrier mobility might sensibly limit the prospects of graphene on SiC(0001). In this work we pre-sent and discuss two different approaches that allow for a precise tailoring of the band-structure of graphene on SiC(0001): non-covalent functionalization of the graphene surface with a strong acceptor molecule, i.e. tetrafluorotetracyanoquinodimethane (F4-TCNQ), and passivation of the SiC in-terface via hydrogen intercalation. Both approaches effectively eliminate the in-trinsic n-type doping in graphene and might have a positive impact in the charge carrier mobility. The molecular functionalization approach also leads to an en-largement of the band-gap of bilayer graphene to more than double of the original value. Hydrogen intercalation yields graphene layers decoupled from the SiC substrate and hence quasi-free standing. Furthermore, this work investigates a combination of the two approaches and demonstrates that quasi-free standing bilayer graphene can be hole doped by depositing F4-TCNQ.