The Cleveland Cavaliers hope they took another step toward keeping LeBron James. The New York Knicks are in better position for a run at him — and a second superstar, too.

And they aren’t the only team lining up for a chance to become a summer spender.

The Knicks acquired former scoring champion Tracy McGrady on Thursday in a three-team swap with the Houston Rockets and the Sacramento Kings. The deal left them on the verge of being able to offer two maximum salary contracts to the 2010 free agent class that could be headlined by James.

Amare Stoudemire could be in the market for one if he decides to leave Phoenix — where he’ll again finish the season after spending the weeks before the deadline atop the trade rumor mill.

“I’ve maintained that unless there was something out there that improved our team and put us in a lot better position moving forward, then we weren’t going to do anything. And that was the case,” Suns general manager Steve Kerr said.

Chicago, Washington and Sacramento all cleared enough salary in moves before the 3 p.m. EST deadline to be able to afford a max player, and the Los Angeles Clippers got close.

The Cavaliers gave James more reason to stay home. They acquired forward Antawn Jamison on Wednesday, a deal that could make the Eastern Conference leaders even stronger.

“We’re trying to build a franchise that all players want to be a part of, that can have sustainable success and do things at a high level,” general manager Danny Ferry said. “Clearly LeBron’s an important player for Northeast Ohio, for Cleveland, for the Cavaliers. It’s all ground in winning, too. Antawn can help us win. We’re excited what he can bring to us over the next few years.”

The Knicks can afford James and perhaps someone else in the class that could include Dwyane Wade and Chris Bosh.

By including Jared Jeffries in the deal for McGrady, whose $22.5 million contract expires after this season, the Knicks removed $6.9 million from next season’s payroll and left them with about $32 million in salary cap space. Those top free agents would each earn a little more than $16.5 million in the first season of a max deal.

“Let’s put it this way. I think this gives us flexibility. A lot of flexibility in a lot of different directions,” Knicks president Donnie Walsh said. “I know everybody is focused on individual players, but we’re not. We’re focused on putting together the best team we can. So that takes a lot of different directions and we have a lot of time to figure out which way we’re going to go, but it is a lot of cap space.”

In the meantime, the Knicks hope McGrady can lead them into the playoff race. He’s only played six games this season after returning from knee surgery, but is convinced he has plenty left.

“I can’t wait to get back on the court to continue doing what I love to do,” McGrady said in a statement on his Web site. “I am excited to be headed to New York and look forward to wearing a Knick uniform. I know that I can and will contribute to this organization. It’s a dream to play in New York and there is nothing that compares to playing in the Garden.”

To get him, the Knicks sent Jeffries and rookie Jordan Hill to Houston along with a protected first-round pick in 2012, and gave the Rockets the right to exchange first-round picks in 2011. The Rockets will get high-scoring guard Kevin Martin and forward Hilton Armstrong from Sacramento, while the Kings received Larry Hughes from the Knicks, Carl Landry and Joey Dorsey from Houston and sent guard Sergio Rodriguez to New York.

The Knicks also dealt Nate Robinson to Boston along with Marcus Landry for Eddie House, J.R. Giddens, Bill Walker and a future conditional second-round pick.

The Bulls were busy, trading power forward Tyrus Thomas to Charlotte for a future, protected first-round pick and the expiring contracts of guards Flip Murray and Acie Law.

Chicago also dealt guard John Salmons to Milwaukee for Hakim Warrick and Joe Alexander, whose contracts also are expiring.

“You can see the price to be paid to gain flexibility and in a lot of cases, it was very, very high. You’ve got to give something to get something,” Bulls GM Gar Forman said. “That’s why I think we feel so good today that we kept the nucleus intact, our starting lineup intact, and yet gained the type of flexibility that we wanted to gain to make that next step in the process we wanted to make this summer.”

The Wizards and Clippers also shed salary in the three-team deal that sent Jamison to the Cavaliers. They joined the Knicks, New Jersey Nets, Miami Heat and Bulls as the teams with the most money available.

Also Thursday:

—The Utah Jazz traded shooting guard Ronnie Brewer to the Memphis Grizzlies for a future first-round draft pick.

— Milwaukee made a second trade, sending rookie guard Jodie Meeks and center Francisco Elson to Philadelphia for guard Royal Ivey, center Primoz Brezec and a second-round pick in the 2010 draft.

—Sacramento acquired swingman Dominic McGuire and cash from Washington for a protected 2010 second-round pick.

—The Bobcats made another minor trade, acquiring veteran big man Theo Ratliff from San Antonio for a second-round pick.