CLEARWATER, Fla. — The competition for the Phillies to sign Bryce Harper intensified Wednesday when the team learned that the San Francisco Giants were the second organization in three days to fly to Las Vegas for a meeting with the free agent.

The Giants, once considered the Phillies’ biggest threat to sign Harper before seemingly falling of the race, met with Harper and agent Scott Boras on Tuesday. The meeting, first reported by the San Jose Mercury News, was the team’s second with Harper this month.

The Phillies felt confident last week that they would sign Harper, as they were motivated from missing on Manny Machado and knew what the perception would be if the offseason ended without a superstar on their roster. That confidence grew over the weekend, when owner John Middleton flew his private jet to Vegas for a meeting with Harper and Boras.

The Phillies already believed they would be the highest bidder for Harper. Then the market moved even more in their direction as potential suitors began to fade away.

But that confidence was short-lived. The Phillies learned Monday morning that the Dodgers visited Harper on Sunday in Vegas, arriving roughly 24 hours after Middleton had left town. The Phillies, after they began to feel like the only player left at the table, had competition. And that competition grew Tuesday when the Giants landed in Vegas.

Harper longs to play on the West Coast, but his two California suitors have been thought to be leery of signing him to the decade-long pact that he seeks. Perhaps the Giants or Dodgers have changed their thinking or Harper has softened his stance to play closer to home.

The Phillies are believed to be the team most willing to give Harper both the longest deal and the most money, but perhaps the Dodgers and Giants could win Harper’s services by giving him a short-term deal with an extremely high annual value. If so, Harper would not be able to eclipse the $300 million deal that Machado signed last week with the Padres or the $260 million extension that Nolan Arenado scored from the Rockies.

But Harper and Boras could claim a victory if his contract carries a higher average annual value than those two megadeals. A three-year deal would allow Harper to become a free agent again when he’s 29, just one year after Mike Trout is slated to enter free agency. Harper, if he has to settle for a shorter contract to stay out west, could then try again to set records.

The Phillies still believe they have a chance to land Harper, but their confidence is not nearly as high as it was just a week ago. The Nationals, Padres, and White Sox all seemed to distance themselves last week from the Harper sweepstakes. The Phillies were in the driver’s seat when Middleton’s private jet left Florida for Vegas.

But what they did not know was that the Las Vegas airport would be ushering in two more teams, suitors they had believed to be out of the race. The competition has stiffened.