We have studied the effect of different supports (CeO₂, ZrO₂, SiC, SiO₂ and Al₂O₃) on the catalytic performance and phase stability of Co₃O₄ nanoparticles during the preferential oxidation of CO (CO-PrOx) under different H₂-rich gas environments and temperatures. Our results show that Co₃O₄/ZrO₂ has superior CO oxidation activity, but transforms to Co⁰ and consequently forms CH₄ at relatively low temperatures. The least reduced and least methanation active catalyst (Co₃O₄/Al₂O₃) also exhibits the lowest CO oxidation activity. Co-feeding H₂O and CO₂ suppresses CO oxidation over Co₃O₄/ZrO₂ and Co₃O₄/SiC, but also suppresses Co⁰ and CH₄ formation. In conclusion, weak nanoparticle-support interactions (as in Co₃O₄/ZrO₂) favour high CO oxidation activity possibly via the Mars-van Krevelen mechanism. However, stronger interactions (as in Co₃O₄/Al₂O₃) help minimise Co⁰ and CH₄ formation. Therefore, this work reveals the bi-functional role required of supports used in CO-PrOx, i.e., to enhance catalytic performance and improve the phase stability of Co₃O₄.