And proven veterans like Tom Watson, Tom Kite, Curtis Strange and Raymond Floyd warrant consideration, as do a handful of newcomers and those who may fall just shy of earning enough points to make the Top 10.
Stockton said the increasing options have been the first "unfun" aspect of his captaincy.
"I'm going to make two players happy and five or six unhappy," he said.
Six players -- Fred Couples, Payne Stewart, Lanny Wadkins, Hale Irwin, Paul Azinger and Corey Pavin -- have clinched berths on the team.
This week's PGA Championship at Crooked Stick is the final event in which players can earn points. Stockton's selections will be announced Tuesday; the Ryder Cup matches will be Sept. 26-29 at Kiawah Island, S.C.
Mark O'Meara, Mark Calcavecchia, Wayne Levi and Tim Simpson rank seventh through 10th with Steve Pate, Kite, Beck and Gil Morgan 11th through 14th.
Stockton said the ideal scenario would be for all the contenders to finish in a tie, fly to South Carolina and have an 18-hole playoff for the remaining spots. Realistically, however, Stockton will have to make a difficult call.
"I'll take the Top 10 and then two I think fit the team," he said.
Regardless of what the final 12-man roster looks like next week, "I have no qualms this team will be ready to play and I don't think there will be a weak link."
Despite the evolution of Nicklaus as a sentimental favorite, Stockton said the Golden Bear is "still more of a long shot than some of the younger guys."
Stockton also said Payne Stewart's contention that the stamina to play 36 holes be among criteria for selection has merit.
"The golf course is very difficult to play 36 holes on if you're 21 years of age let alone 50. I played 18 holes, rode in a cart and was still tired," Stockton said.
Stewart said his comments weren't meant to demean Nicklaus.
"Jack Nicklaus is the greatest golfer who ever lived," Stewart said. "I wasn't trying to put Jack Nicklaus down, so I'm just going to leave that issue at rest."
Paul Azinger, in the midst of a comeback from shoulder surgery, withdrew from the PGA Championship yesterday. He was replaced by Doug Tewell. Other late additions include Keith Clearwater, Dave Barr and Mark Wiebe.
British Open champion Ian Baker-Finch is suffering from back spasms and may be forced to withdraw.
Baker-Finch walked off the course after only three holes of a practice round yesterday.
"I'll see how it feels tomorrow," he said. "If it isn't better, I'll have to pull out. I can't play the way it is now."
Jose Maria Olazabal had a hole-in-one on the 212-yard, par-3 17th during his practice round yesterday.
In what has become commonplace at the PGA, complaints surfaced about the difficulty and length of the course.
At 7,289 yards, Crooked Stick will be the second-longest PGA site ever.
"It's just extremely long," Irwin said. "They may need to bring it up just to get everybody in and out."
The longest course was Columbine Country Club in Denver, site of the '67 PGA.
Stockton said the PGA Championship will have a major impact on his wild-card selections.
"I'd like to see some people come out of here with some good vibes," he said. "This is a major and you want to see who can breathe at the end of the week."
Historically, the PGA Championship has been a sweltering, blistering affair.
But the temperatures yesterday were in the mid-60s and rain dampened Crooked Stick. Rain is a possibility for practice rounds again today with a clear forecast for the weekend.