The use of molecular materials in solar cells and nano-electronics demands a fundamental understanding and control of their electronic properties. Particularly relevant is the molecular response to the environment, that is, the interaction with the support and adjacent molecules, as well as the influence of electrostatic gating. Here, the control of molecular level alignment and charge states of fluorinated cobalt phthalocyanines (F16CoPc) on atomically thin hexagonal boron nitride (h-BN) sheets on Cu(111) is reported using scanning tunneling microscopy (STM) and spectroscopy (STS), as well as atomic force microscopy (AFM) and complementary density functional theory (DFT) calculations. Three parameters that govern the electronic level alignment of F16CoPc orbitals are investigated: i) template-induced gating by the work function variation of the h-BN/Cu(111) substrate, ii) gating by the STM tip, and iii) screening by neighboring molecules. The interplay of these parameters influences the charge distribution in the studied molecular arrangements and thus provides the possibility to tune their physicochemical behavior, for instance, the response toward electronic or optical excitation, charge transport, or binding of axial adducts.