We show that in Pt/CoFeB/HfO2 a wide range of oxidation levels at the ferromagnet/oxide interface can be accessed through magneto-ionic gating using ionic liquid gates. Perpendicular magnetic anisotropy (PMA) is induced at intermediate oxidation levels, while two in-plane anisotropy states with nonequivalent ionic states are induced for under-oxidized and over-oxidized interfaces. This system shows reversibility and non-volatility in the whole range of oxidation states, where oxidation levels have been monitored by x-ray absorption spectroscopy and x-ray photoelectron spectroscopy. This study shows that multistate magneto-ionic memory elements with a wider range of intermediate states can be designed by leveraging both under- and over-oxidation around the optimal oxidation state that induces PMA.