Working on the previous alternate version of Chess suggested to me a problem with various extended versions I have toyed with in the past.
Adding extra pieces changes the character of the game, by making Castling no longer as useful as in the conventional game of Chess.
This illustration shows how this can be avoided:
Here, the conventional array is extended only by the addition of one new piece, the Camel, which has a move like that of the Knight, but extended, so that its move displaces it by three squares in one orthogonal direction, and one square in a perpendicular orthogonal direction.
So the Kingside Bishop, Knight, and Camel all bring their force to bear on the square in front of the King, and the Queenside ones to the square in front of the Queen, following the pattern of the conventional array.
The other new pieces added to give the game new interest are placed in wings on the side of the board, following the scheme often used for four-handed Chess.
In order to make this symmetrical, it is necessary to switch the Black King and Queen (well, the White ones could have been switched instead, but let's not get into that). And, of course, this depicts how the character of the game is still profoundly changed from that of regular Chess.
While Castling isn't changed much, since the Pawns on the side don't need to be advanced to get some of the new pieces out of the way to allow Castling, now each player has a group of additional pieces on his Kingside, while the additional pieces of the opponent bear on his Queenside. In regular Chess, Castling to the Queenside is only slightly inferior to Castling to the Kingside; here, the Kingside and Queenside are not at all equal.
In this diagram, the extra pieces I've added to give new piquancy to the game happen to be a Cannon, a Tiger (a Bishop-mover/Knight-capturer), a Man (a piece with the move of the King but no royal powers), and a Walker (my name for the Berolina Pawn - a Wazir-mover Fers-capturer). In front of them I show four checkers, but in this case they may merely represent Pawns that move sideways, and promote on the extreme Queenside edge of the board.
The problem of creating an imbalance between the Kingside and Queenside can be solved by adding only two new pieces to the board, but then, despite the fact that the Castling issue is fixed, people will be tempted to view adding the wings to the board as excessive:
At least the Kings and Queens are facing each other, as in regular Chess, again.
This layout, though, has a fatal problem: unless enemy pieces obligingly move to just the right square to be captured by the Tiger's Knight's move, the Tiger can't move from its starting square, because it normally moves diagonally. Of course, that can be solved by adding a different new piece, one that moves more like a Rook, instead of the Tiger. Or, one could give the Tiger a special first move of two steps forward as another way around the problem.
One could add three new pieces, and keep the alternate symmetry of the Kings versus the Queens, for a compromise board:
The Kingside and Queenside are not entirely balanced, but at least the imbalance is not nearly as great as before, and the Tiger can move normally from its starting square.
Of course, with sideways-moving Pawns now moving in both directions, they would have to be distinguished somehow; or the checkers could be given some other move, such as making them Walkers, or some type of piece that does resemble a checker, but moves forwards or backwards and doesn't promote.