The only card I can think of is the AA Citi Executive card which gives access to Admirals Clubs when flying AA/oneworld and partner lounges when flying AA. The Admirals Clubss aren't great, but the only other cards in the US that give lounge access beyond PP are the Amex Plat (Plaza Premium-affiliated lounges, DL when flying DL, Centurion, Escape, Lufthansa when flying LH group airlines, maybe one or two add'l minor options I'm forgetting about), Venture X Visa (Plaza Premium and the Cap One lounges which is expected to be open in DFW/IAD/DEN by the end of the year), United Club Visa (Star alliance lounges when flying a *A airline), and DL Reserve Amex (DL lounges when flying SkyTeam + Centurions, not worth the card unless they would take advantage of the annual companion ticket and/or the DL elite mileage bonuses).

Chase will have their Sapphire lounges open in the near-ish future (about 8 in the pipeline), but no specific opening dates yet and they may be Priority Pass-affiliated (yet to be determined if it will exclude PP Select that is offered with US credit cards and/or if there will be additional benefits for those entering with their Sapphire card).