BacCanCat

That suggested a 4-player variant with 6x6 camps in the corner, a Pawn rank turning the corner at cell ff/fk/kf/kk, and the King at the turn in the "behind-the-Pawn" rank, i.e., cell ee/el/le/ll (aa-ap is the left edge, aa-pa the bottom edge, ap-pp the right edge, and pa-pp the top edge). This allows Kings to:
Castle "Kingside" with Rooks on be/bl/eb/eo/lb/lo/ob/ol;
Castle "Queenside" with Rooks on ae/al/ea/ep/la/lp/pb/pl;
Cathedral "Kingside" with Bishops on bb/bo/ob/oo;
Cathedral "Queenside" with Bishops on aa/ap/pa/pp.
To provide each army with Bishops on the opposite binding the obvious place to put these was ab/ao/ba/bp/oa/ap/pb/pa. I also decided to replace the middle five (out of 11!) Pawns with Yeomen so that they were to the opposite-colour army what the two remaining Pawn groups were to the adjacent-colour armies. That gave a nice tidy arrangement of 1 King + 11 FO Divergents + 8 linepieces = 20 pieces aside.

The next stage was to fill in each camp's 16 empty spaces. I considered the Carrera/Capablanca pattern of Knights+Queens+Marshals+Cardinals, or even reflecting the much larger board size with Camels+Queens+Canvassers+Caliphs or Zebras+Queens+Zebshals+Zerdinals (see my article Man and Beast 08: Diverse Directions). As four of each compound aside seemed excessive, I rejected this idea. Then I thought of Knights and Camels, or Zebras and Zemels. At the time of posting I had settled on having one subvarant with each pair, but since then I have consider two more subvariants. One has the Catapults (Knight+Trebuchet) and Campers (Camel+Tripper) of Nearlydouble Chess and its offdshoots, and one the Gazelles (Knight+Zebra) and Cogazelles (Camel+Zemel) that I recommend for Nearlydouble version of any Knighted-piece game. Either way there are four of each aside, the colourswitching leapers being between King and Rooks and the colourbound ones in a single block between King and Bishop block.

That left two four-cell blocks to fill. Ecumenical pieces, I wondered - Queen/Marshal/Canvasser/Gnu/2 Caliphs, or their Zebra equivalents, aside? Well, I'd have to have, say, 2 Gnus and Canvassers aside as well, or two empty cells, and it would ruin the symmetry. Instead I decided to use a third paired-by-direction group - Cannons behind the Rooks and Arrows in front of the Bishops, clustering radial pieces by direction. Thoughts of representation gave me the idea of including compound pieces - just those of two duals, as used in Wildeurasian Qi - in a communal Reserve. Allowing promotion to these and a "win by marriage" gives this variant its name - short for Bachelor, Cannon, and Cathedralling.

Setup

RESERVE

In theory 40 Pawns and 44 Yeoman could also be considered in Reserve, but in practice I do not expect these to get used up.

Pieces

Steppers, 12 aside, 36 on board altogether, 84 in Reserve:

	PAWN: "Forward" is taken as toward the completely enemy edge on the same side of the long diagonal through the camp. Pawns can move one step either orthogonally toward that edge without capturing, or diagonally toward it to capture. Pawns can never cross the long diagonal through their own camp. Represented by White Pawns.
	YEOMAN: These pieces usually play quite differently to Pawns as their reversal of Pawn divergence usually results in two noncapturing and one capturing move. In this variant, however, they preserve the forking ability. Their noncapturing move is one step on or parallel to the long diagonal through, and away from, their camp. They can capture by making either of this move's orthogonal components. Represented by Black Pawns.
	KING: Moves one step in any radial direction. Must be kept out of check, with checkmate and stalemate as per FIDE Chess. Represented by White Kings.

Linepieces, 8 aside, 32 on board altogether, 8 in Reserve:

+=	ROOK, BISHOP, QUEEN: the familiar FIDE long-range pieces. Bishops are confined to cells the same colour as their starting ones. Queens are in Reserve. Represented by the White form of themselves.

Hoppers, 8 aside, 32 on board altogether, 8 in Reserve:

	CANNON: Moves like a Rook, except that capturing requires exactly one intervening piece, which may be of either army and is not itself captured. Represented by Black Rooks.
	ARROW: Moves like a Bishop, including confinement to cells of one colour each, but again capturing requires exactly one intervening piece, which may be of either army and is not itself captured. Named by Fergus Duniho for Yang Qi. Represented by Black Bishops.
	TANK:: The compound of Cannon and Arrow, it moves like a Queen, but again capturing requires exactly one intervening piece, which may be of either army and is not itself captured. Name an extrapolation from Cannon and Arrow. Represented by Black Queens.

variant 1 leapers, 8 aside, 32 on board altogether, 8 in Reserve:

	KNIGHT: Makes 2:1 leaps. Represented by White Knights.
	CAMEL: Makes 3:1 leaps. Represented by Black Knights.
	GNU: Makes 2:1 and 3:1 leaps. Represented by Black Kings.

Variant 2 leapers, 8 aside, 32 on board altogether, 8 in Reserve: For the above pieces this variant substitutes the ZEBRA, which makes 3:2 leaps; ZEMEL, which makes 5:1 leaps; and ZEBU, which makes both.

Variant 3 leapers, 8 aside, 32 on board altogether, 8 in Reserve: For the above pieces this variant substitutes the CATAPULT, which makes 2:1 and 3:0 leaps; CAMPER, which makes 3:1 and 3:3 leaps; and ACHATES, which makes all four.

Variant 4 leapers, 8 aside, 32 on board altogether, 8 in Reserve: For the above pieces this variant substitutes the GAZELLE, which makes 2:1 and 3:2 leaps; COGAZELLE, which makes 3:1 and 5:1 leaps; and GALLOP, which makes all four.

Rules

Pawns and Yeomen reaching a completely enemy edge are promoted to any stronger piece in Reserve. The following pieces may also be promoted when capturing if the relevant promotee is in Reserve:
a Rook capturing a Bishop, or vice versa, to Queen;
a Cannon capturing an Arrow, or vice versa, to Tank;
a Knight capturing a Camel, or vice versa, to Gnu (variant 1);
a Zebra capturing a Zemel, or vice versa, to Zebu (variant 2).
a Catapult capturing a Camper, or vice versa, to Achates (variant 3);
a Gazelle capturing a Cogazelle, or vice versa, to Gallop (variant 2).

A King on its starting cell may Castle with any unmoved Rook of its own army, Cathedral with any unmoved long-diagonal Bishop of its own army, or do either with either becoming a Queen through capture 3 or 4 steps away from the King in any radial directtion. In each case the King moves two steps toward the linepiece, which moves to the cell halfway between the King's start and end cells, both through otherwise unoccupied cells. This last rule keeps notation unambiguous: ee-ec is with the eb Rook if it is there, with the ea one only if eb is empty. The King may not Castle or Cathedral into, out of, or through Check. The King can return to its starting cell and Castle or Cathedral again, but the linepieces must be unmoved since the start or since promotion.

A player whose King is en prise to the player about to move is Checkmated and their pieces go into Reserve. The Checkmating player then makes their move and play proceeds with the remaining players. The first player Checkmated loses and the player delivering the third Checkmate wins. An alternative way for a player to win is by bringing together a King, Queen, Tank, and Gnu of their army in any square of four adjacent cells. This is like the "win by marriage" of Bachelor Chess and Bachelor Kamil but scaled up for a much larger army. Finally a player can also win by moving a Pawn or Yeoman to a promotion cell when there are only Pawns and Yeomen in Reserve, which actually gets harder as players get checkmated.

In a series of games there is a total score of 6 for each game. Players score:
0 if they drop out of the game when they are one of 4 players;
1 if they drop out of the game when they are one of 3 players;
2 if they drop out of the game when they are one of 2 players;
the remainder for winning the game. This figure will usually be 3 but could be:
4 if they win by uniting four compounds when only one player has been Checkmated;
6 if they win by uniting four compounds when no player has been Checkmated.

Notes

instead of Knight/Camel/Gnu:
Nightrider/Camelrider/Gnurider;
Rose/Macel/Ung, curved versions of the above;

instead of Cannon/Arrow/Tank:
Gryphon/Anchorite/Gorgon;
Girlscout/Boyscout/Doublescout.