The 10-file MITREGI 90 is my attempt at a Shogi with an equivalent change to the Bishop in Europe. The 12-file MITREGI 108 is to Mitregi 90 what Modern Kamil and Wildebeest Chess are to FIDE Chess, and Bachelor Kamil is to Bachelor Chess. The name combines the English name of the main additional piece (Mitre) with a Japanese suffix indicating a Shogi-like variant (-gi), although it can also be interepreted as the German for with (Mit) followed by the dative of the Latin rex, meaning King (regi), referring to there being a number of generals "with the King". However you pronounce it, a hard G is recommended - consistent with Shogi itself, Gimli and Gil-galad, Gyre and Gimble, and Gilman. Both still have 9 ranks. This is not to say that Shogi itself is a less than excellent game or needs "improvement"; I am aware of the dangers of such claims. However these variants do, I hope, bring a quality of their own while not detracting from those of Shogi to the extent that variants adding entirely different kinds of piece (e.g. Blind Tiger, Side Mover) do. I have also now added two 12-rank variants, Mitregi 120 and Mitregi 144, which have larger armies with additional symmetric pieces. I have also created a 3d variant along similar lines, Tunnelshogi, which has its own page.
In Shogi the diagonal pieces are replaced by two short-range "generals" each combining a symmetric move in one radial direction with a forward-only (FO) move in the other. The first-rank Rook and Knight have been reduced to their forward moves. However a single full Rook has reappeared, and a Bishop appeared, on the second rank. The whole set-up is highly dependent on promotability of most pieces and reintroduction of captured ones. Without these one Bishop cannot cover the board, and there is no colourbound counterpart to any FO piece. For ease of extrapolation my terminology is a radical departure from traditional translations, fully explained in my piece articles Constitutional Characters and From Ungulates Outwards.
POINT (Fuhyo=Foot Soldier): This is the Shogi (and Xiang Qi) replacement for the Pawn, and until promoted it always moves one step ortogonally forward. Points start on the third square of the two leftmost, two rightmost, and two middle files.
CROSS (Sekisho=Stone General): This is the Point's colourbound analogue, and until promoted it always moves one step diagonally forward. Crosses start on the third rank on those squares not occupied by Points. This mixture of Pawnlike pieces introduces a distinctive version of the Pawn structure of Occidental standard games so lacking in Shogi.
ROOK (Hisha=Flying Chariot): This is the piece that reappeared in Shogi in a different location. It moves any distance orthogonally, but cannot pass through an occupied square. Shogi has but one Rook, but Mitregi increases it to two, on the second square of both second outermost files. This positioning means that, as in Shogi itself, there is no castling.
WING (Kyoosha=Fragrant Chariot): This is the piece that replaced the Rook in Shogi in its original location. It moves like a Rook, but only in the one forward direction. In Mitregi as in Shogi, the Wings start on the corner squares.
KNIGHT (N/A): This piece makes a 2:1 leap in any of up to eight directions. It is not used in Shogi or its traditional variants, or in the 9-rank versions of Mitregi. In the 12-rank versions they start on the second square of both third outermost files.
HELM (Keima=Honourable Horse): This is the piece that replaced the Knight in Shogi. It moves like a Knight, but only in the two forwardmost directions. In Mitregi as in Shogi, the Helms start on at the end of both second outermost files.
BISHOP (Kakugyo=Angle Mover): This is the piece that appeared in Shogi independently of its European use. The Rook's colourbound analogue, it moves any distance diagonally, but cannot pass through an occupied square. Shogi has but one Bishop, but Mitregi increases it to two, on the second square of both fourth outermost files.
MITRE (N/A): This piece is the Wing's colourbound analogue, moving like a Bishop but only in the two forward directions. It is not used in Shogi or its traditional variants. In Mitregi the Mitres start at the end of both third outermost files.
CAMEL (N/A): This piece is the Knight's colourboubnd analogue, making a 3:1 leap in any of up to eight directions. Mitregi 144 is (at the time or writing) the only Shogi-based variant using this piece, which starts immediately in front of both Silvergeneral.
HUMP (N/A): This piece is the Helm's colourbound analogue, moving like a Camel, but only in the two forward directions. It is not used in Shogi or its traditional variants, or in the 10-file versions of Mitregi. In the 12-file versions they start at the end of both fourth outermost files.
SILVERGENERAL (Ginsho): This is a Shogi piece combining the Ferz and the Point. These start at the end of both second innermost files and in Mitregi, unlike in Shogi, are unpromtable. In addition Crosses, Mitres, and Humps are promoted to Silvergenerals.
GOLDGENERAL (Kinsho): This is a Shogi piece combining the Wazir and Cross. Unlike Shogi, Mitregi has but one Goldgeneral aside, at the end of one of the two middle files. This is partly to make the number of files even, but partly because the Goldgeneral was the Japanese replacement for the Ferz which the Chinese had duplicated, and so reverses that duplication. As in Shogi it is unpromotable. In addition Points, Wings, and Helms are promoted to Goldgenerals.
KING (Japanese name varies between armies): This is the one piece surviving entirely unchanged from Chaturanga. It occupies the end of the other middle file. It can move one square in any orthogonal and diagonal direction, is unpromotable, and must be kept out of check.
CHATELAINE (Ryuo=Dragon King): This piece is the Rook promoted to have the Ferz move added. In Mitregi as in Shogi it is not an array piece.
PRIMATE (Ryuma=Dragon Horse): This piece is the Bishop promoted to have the Wazir move added, thereby removing its colourbinding. In Mitregi as in Shogi it is not an array piece.
GNU (N/A): This piece is the Knight or Camel promoted to have the other's move added. It is not used in Shogi or its traditional variants, or in 9-rank versions of Mitregi, and in 12-rank versions it is not an array piece.
The balancing principle determines promotion and reintroduction rules. All varieties of general are unpromotable, and FO colourbound pieces are promoted to Silvergeneral. It follows from the Hump's limited move that it must be promoted on reaching the enemy camp, which it does on its second move from the array! As in Shogi, pieces are reintroduced UNPROMOTED, on ranks where prootion would not immediately be required - the entire enemy camp in the case of Humps. They are further restricted by a player being forbidden from exceeding the following UNPROMOTED pieces: (1) 1 Point on a file; (2) the array number of Crosses on one cell colour - 4 in Mitregi 90 and 120, 6 in Mitregi 108 and 144; (3) 2 of EACH other colourbound piece on one cell colour. Note that Points CAN be reintroduced on files that had none in the array, just as Helms can be placed on the even ranks which they cannot reach from the array.
There is much to be said for a chequered board because of the above restrictions. If Shogi pieces are being used two sets are required, with 24 or 28 pieces in use and 16 or 12 spare. You could flip standard pieces for the extras, mark promotion by putting a spare underneath, and hope that you don't run out of spares! Rooks and Bishops might still be flipped for promotion to ameliorate that problem. If you wish to make pieces with Europeanised markings for the Europeanised games I can suggest the following: King/Rook/Bishop: large symbols; Chatelaine/Primate: small Bishop/Rook inside large Rook/Bishop; Goldgeneral/Silvergeneral: small Bishop/Rook behind small Rook/Bishop; Wing/Mitre: small Rook/Bishop behind forward arrow; Helm/Hump/Point/Cross: small Knight/Camel/Rook/Bishop behind empty space.