I know PAE is technically in Everett, but if you want to get that technical then Seattle has no airports as SEA is in the city of Sea-Tac.
So the main focus should be on AS's strategy for the existing 2nd airport at PAE. Time will tell if its a success I suppose, but I think the region is a long way off from needing a 3rd airport. Maybe someday if 520 is extended another 7-8 miles to Novelty they could put an east-side focused airport out there.
But when you look at US cities with 3 or more airports, you're looking at what? San Francisco, Los Angeles & New York?