We demonstrate that the intrinsic electron doping of monolayer epitaxial graphene on SiC(0001) can be tuned in a controlled fashion to holes via molecular doping with the fluorinated fullerene C60F48. In situ angle-resolved photoemission is used to measure an upward shift of (0.6 ± 0.05) eV in the Dirac point from −0.43 eV to +0.17 eV relative to the Fermi level. The carrier density is observed to change from n ∼ (1 × 1013 ± 0.1 × 1013) cm−2 to p ∼ (2 × 1012 ± 1 × 1012) cm−2. We introduce a doping model employing Fermi-Dirac statistics which explicitly takes temperature and the highly correlated nature of molecular orbitals into account. The model describes the observed doping behaviour in our experiment and readily explains why net p-type doping was not achieved in a previous study [Coletti et al., Phys. Rev. B 81, 8 (2010)] which used tetrafluorotetra-cyanoquinodimethane (F4-TCNQ).