What are the properties of COₓ where x ≥ 3?
At least the trioxide $\ce{CO3}$ exists, and it has even been detected in at least two isomeric forms.  Wikipedia reports that it forms as a transient species in reactions between carbon dioxide and atomic oxygen or ozone, in irradiation of solid carbon dioxide, and even in oxidation of carbon monoxide by $\ce{O2}$.