The Cardinals increased their offer to free-agent first baseman Albert Pujols on Tuesday on hopes of retaining the three-time National League MVP. The new deal is believed to approach $220 million for as many as 10 years. The Marlins and a mystery team are also in serious pursuit of Pujols. St. Louis declined to place a deadline on their offer, but Miami is believed to be pushing for a resolution before the meetings adjourn Thursday.