One deck of SET® cards, and 2 or more players. Not recommended for novice players, because it may be a little confusing for folks who haven't quite solidly figured out what a Set is yet.
A near-set is 3 cards that could be a Set if you were to change one property of one card. For example, the following is a near-set:
This particular near-set is a "shape-near-set", because shape is the property that must be changed on one card to make this a Set. Note that you can change the shape on any one of the three cards to make a Set. This is always true of near-sets.
Play like regular SET®, except look for near-sets instead of Sets. We still say "SET!" when we find one, though, because it's easier than "NEAR-SET!".
Once you're used to the idea of "near-sets", this game is very easy -- almost impractically so. For a harder variant, decide beforehand on a particular property on which to base your game. For example, you might only look for number-near-sets.
In regular SET®, if you choose two cards, there is exactly one other card in the deck that will match up with it to make a Set. In Near-Set, if you choose two cards, there are up to eight other cards in the deck that will match up with it to make a near-set. This means near-sets turn up much more frequently than Sets.
The first time we played Near-Set, we almost never had 12 cards on the table. One of us would find a near-set before we finished laying out 12 cards; and then one of us would often find another near-set before we finished replacing the 3 cards that were just removed. The game moved very quickly, almost confusingly so.
In the "harder variant", if you choose two cards, there are at most two other cards that will match up with it to make a near-set of the chosen type. The chosen type of near-sets turns up with a frequency much closer to the frequency of Sets in regular SET®. They still show up slightly more often, but this is offset by the fact that you're not accustomed to finding near-sets, so they're a little harder to recognize.