Normally, any team can only afford 2 big contracts

Ideally, a contending team would have 2 big stars with max contracts, plus bunch of quality young uprising players, and a few veterans with minimum pay. However, this is not an ideal world, and with the intense competition, one would hope to get a 3rd big gun relatively cheaper. That 3rd option would either be a veteran who has just passed the prime, has made his money, and wants to play for a contender for less, or a young talent whose contract is limited by rules and years.

If an owner is willing to spend and pay the extra luxury tax, if he sees the opportunity, he would be willing to spend more for a lease - pay extra for one year or two, try to seize the opportunity and get it done. He might be able to stack up a few big names for short contracts.

If a ball club is rich in tradition and harmony, where your franchise player is willing to take some sacrifice to allow the team to attract more good players. As posters pointed out that TD took a smaller contract than the max he could get (of course not a 30% cut), LeBron has done that as well. He was willing to take a less than max to get Bosh onboard. 15 years ago, Charles Barkley joined Houston Rockets for cheap, and left room for the team to get Scottie Pippen. Unfortunately, Pippen brought anything but success. He was distraction on and off court, constantly complaining about his touches and shots.

Spurs is the perfect successful example. Heat is getting what they wanted - a 3-headed monster, but their bench is thin. Even that, it was only made possible because Haslem accepted a much smaller contract. 

The Knicks on the other hand, is famous/imfamous for their habit of piling up bad contracts - Strawberry, Curry, Crowford, and Randolph etc in the past. Any club, if they have some bad contracts to unload, the first thing they will automatically think of, is to call Knicks. As of now, Melo and Amare are signed with the max or close to max contract for 20 million a year, till 2016 and 2015 respectively. Tyson has 3 years left for 15 million a year. That's the maximum of maximum in terms of size and length for your big 3 players. All there left is pocket changes for the rest of 10 players. 

Instead of looking for young un-noticed players hoping for undiscovered rough diamond or washed up veterans for cheap leasing against time, NY media is fantasizing about Steve Nash. They should really put down whatever they are smoking. I know they need to write something for a living, and they need to come up with stories to fill the void of the starting of fishing season. But boy, Steve Nash? They can't even afford JR smith.

Knicks can't afford anyone has a name that non-basketball fans is semi-familiar with.