I don't know what the store version is like, but I made a board for 4 way chess between my friends and I once. Basically I added two eight square ranks to each side of the board, making a cross shape.
I found that the Knights became far less influential than they are in the standard game, because the other pieces which go along lines suddenly have more squares (due to the larger board).
Also, your flanks become uncomfortably pressured by the players to your right and left.
I have a three-way chess set, and I've played it on a number of occasions. I imagine four-way chess is slightly less complicated in that things are technically more symmetrical - in three-way chess there's a constant, dynamic force of equilibrium, because if you go ahead the other two will generally league against you...the game is usually won when someone over-commits and cannot pull out of a mating position before his de facto confederate beats him to the mate with his inadvertent help and consequently wins the game.
I've played a version of 4 way chess called "Doubles Chess". The board is octagonal and has 128 squares (although none of the squares are square), and in the middle 8 "squares" came together at their corners. I only played it a few times, but it was kinda interesting. The people across from each other are on a team and the board is made so its hard to move across to the opposite side. Each team has to checkmate both of the other team's kings to win. I didn't play enough to know if it was really any good.
A friend of mine has it. I've played twice and it wasnt overly fun. The diplomacy comes into play but in the end, Rooks, Bishops, and Queens are all that really matter there. Play risk if you want 4 player diplomacy.
One way we have played 4 player chess in the past is to just play regular chess and have each color be a team of 2 players of alternate moves. This is more fun if you don't allow comunication between teammates (or if both are stubborn, arrogant fools like my friends and me).