There are 3 components involved in determining CAT I, II and III capabilities.

a) The aircraft itself has to be equipped with the appropriate avionics and the situation has to be compatible with it. For example, the only aircraft certified to CAT IIIB with one engine out are the MD11, L1011 and A310.

b) The operator (which includes the airline as well as both pilots on board) has to be appropriately rated. I know of multiple instances where a rated relief pilot has been called into the cockpit to serve as the PNF just to satisfy this requirement in lieu of the rostered pilot who was not rated.

c) The airport/runway has to be appropriately equipped. There is no point having a CAT IIIB aircraft trying to make an approach to a runway that supports only VFR operations.

As a result, it is very hard to actually compile a database of CAT compatability.