Common causes of p0345

Does the vehicle ever stall? Is there ever a crank - no start - situation? Has there been a period of time where the engine misfired due to spark plugs or coil issues? The P0345 is unlikely to be representing a failure on it's own; the P0420 and P0430 sound like catalysts that are not working, with means they were likely damaged due to excessive fuel delivery along the way. There's more to the story here, so share what you can about the history of the vehicle and we can try to help.