While the oxidation state Pu(VIII) is shown to be less stable than Pu(V) in the PuO4 molecule, it is not clear if the more electronegative fluorine can help to stabilize Pu(VIII). Our calculations on PuOnF8-2n (n = 0-4) molecules notably confirm that PuO2F4 has both D-1(4h) and C-5(2 nu) minima with the oxidation states Pu(VIII) and Pu(V), respectively, with the latter having lower energy. The hybrid-DFT, CCSD(T), and CASSCF methods all give the same result. The results conform to a superoxide ligand when n >= 2. PuF8 in a O-1(h) state can decompose to PuF6 and F-2, and PuOF6 in a C-1(2 nu) state also can break down to PuF6 and 1/2 O-2. The Pu(VIII) anion PuO2F5- does have a D-5h minimum, which also lies above a C-5(2v), Pu(V) peroxide structure. However, the energy differences between the different minima are not large, indicating that metastable species with oxidation states higher than Pu(V) cannot be completely excluded.