Mutatis Mutandis

My guess and intention is to get a delightful complexity in the gameplay by combining these factors:

1) ideal dimensions of an 8x8 board (neither too much small nor too much large)
2) random setups
3) dropping new pieces every 5 turns
4) mixing exotic with strong and regular pieces
5) using the morph effect

Warning

Setup

The starting setup is determined at random in both boards. The game is played in the left board. Pieces placed on the right board must be dropped in the left board during the game. See the drops performance below in the Rules Section.

Pieces

Queen - It is a compound piece that can move as a Rook or a Bishop. It moves an arbitrary number of spaces in any orthogonal or diagonal direction. It may not pass over occupied spaces, and it ends its move by occupying an empty space or by capturing an enemy piece.
Sissa - It moves each time as Rook AND Bishop following a movement pattern of the form nR+nB or nB+nR, where n is any whole number.

nR+nB means "first n squares like Rook followed by n squares like Bishop";

nB+nR means "first n squares like Bishop followed by n squares like Rook".

Then, if for instance n=5, Sissa MUST MOVE 5 squares as Rook followed by 5 squares as Bishop or viceversa.

There is no restriction on the movement direction of the second stage respecting to the first.

Sissa doesn't leap. All squares it passes by must be empty.

RF - A compound of rook and ferz better known as dragon king; it may move each turn like rook OR like ferz.
BW - A compound of bishop and wazir better known as dragon horse; it may move each turn like bishop OR like wazir.
NG - A compound of knight and guard; it may move each turn like knight OR like a guard [guard=non royal king].
Gryphon - It steps one space diagonally then slides like a rook.
Aanca - It steps one space orthogonally then slides like a bishop.
Rose - A circular nightrider.
Crooked Rook - It is a Rook that must make a 90 degree turn with every step, and must always keep moving away from its starting square.
Crooked Bishop - Also known as Boyscout. It makes one or more successive diagonal steps, but every step must make a 90 degree turn, and every step must be moving away from the starting square. For example, placed on b1 it could move via a2, b3, a4, b5, a6, b7 to a8. It captures as they move, and cannot jump.
NW - A compound of knight and wazir; it may move each turn like knight OR like wazir.
NF - A compound of knight and ferz; it may move each turn like knight OR like ferz.
Rook - Standard rook.
Knight - Standard knight.
Paovao - A compound of cannon and vao.

The following 7 Rococo's pieces move according to the original game, EXCEPTING the restrictions about the edge squares, that is, at this variant they may move freely on the whole board.

Chameleon - It moves passively as an Orthodox Queen. To capture, it mimics the powers of its intended victim. For example, it leaps over a mount to capture a Pawn, withdraws from Withdrawers, approaches Advancers, leaps over Long Leapers, and swaps with Swappers. By the same token, an enemy King standing adjacent to a Chameleon can be captured by the Chameleon. Chameleons can freeze Immobilizers but cannot capture them (but when next to an Immobilizer do not freeze any other pieces). A Chameleon next to a Swapper may capture it (and itself) by mutual destruction.
A Chameleon can use multiple types of capture in the same move. Consider a white Withdrawer on a1, a black Chameleon on a2, a white Long Leaper on a3 and a white Advancer on a5. The Black Chameleon by leaping over the Long Leaper to a4 would also capture the white Withdrawer by moving away from it, and the white Advancer by approaching it (for purposes of approaching and withdrawing it doesn't matter if the move is a slide or a leap). Swaps with Swappers may be combined with other captures.
Long Leaper - It moves as an Orthodox Queen and captures by overtaking. It takes possession of a single intervening piece by leaping to a vacant square somewhere beyond it. It may capture additional pieces, along the same line, if a vacant 'landing square' lies somewhere beyond each enemy piece. A Long Leaper may never jump over a friendly piece, jump over two or more pieces in a row without any empty spaces between, or move to an occupied square.
Swapper - It moves as an Orthodox Queen without capturing, or may swap position with any piece (of either side) an unobstructed Queen's move away. A Swapper may capture an adjacent piece and itself at the same time by mutual destruction. Mutual destruction may not be used when immobilized. If a Swapper swaps with an opposing Swapper or Chameleon, on the following turn the two pieces may not swap back. They may swap again once any other move is made.
Withdrawer - It moves passively as an Orthodox Queen. In order to capture, the Withdrawer must occupy a square adjacent to an enemy piece. To complete the capture, it must move one-or-more squares directly away from the enemy piece. These captures are part of movement, and are not optional -- you can not move a Withdrawer directly away from an opposing piece and not capture it. A Withdrawer may never move to an occupied square.
Advancer - It moves passively as an Orthodox Queen. In order to capture, the Advancer must move to a square adjacent to an enemy piece. If the next square in the direction it moved from the square the Advancer stopped on is occupied by an opposing piece, that opposing piece is captured. (This is capture by approach.) These captures are part of movement, and are not optional -- you can not move an Advancer next to an opposing piece in the line of movement and not capture it. An Advancer never moves into an occupied square.
Immobilizer - It moves as an Orthodox Queen but does not capture. An enemy piece standing adjacent to an Immobilizer may not move while the Immobilizer is present. Black and white Immobilizers, occupying adjacent squares, are each frozen until the other is captured. An immobilized piece other than a King may 'commit suicide' by removing itself from the board (usually to open a line of attack). This counts as a move for the player removing the piece. The Immobilizer may never move to an occupied square.
Cannon Pawn - It moves without capturing two ways: either a single step in any direction, or, it may leap over an adjacent piece of either side to the empty square just beyond. It capture in the second way they move, by leaping over an adjacent piece (the mount), landing on the opposing piece just beyond the mount. If a Cannon Pawn makes a move by itself (rather than being swapped) that lands it on a square on the rank where the opposing King started, then it may promote like if it were a standard Pawn.
Fuge's Archer - The Archer moves as an Orthodox Queen without capturing. It captures by shooting: an Archer can capture an enemy piece an unobstructed QueenÂ’s move away without moving. There is no restriction on shooting an enemy piece adjacent to the Archer or two squares away; for longer shots, some other friendly piece must spot the target by being adjacent to it or two squares away in an unobstructed straight line. An immobilized Archer cannot shoot, but an immobilized piece can spot for the Archer.
Fuge's Shield - The Shield moves as an Orthodox Queen but does not capture. A friendly piece (including the King!) standing adjacent to a Shield is immune from capture. The Shield itself is capturable. The Shield does not protect against immobilization, but an immobilized Shield still protects adjacent friendly pieces. The Shield may never move to an occupied square.
Octopus - From Charles Daniel's Octopus Chess. See a detailed description of its move here.

Mamra - From George Tsavdaris's Mamra Chess. It moves exactly like a nonroyal-King or Guard. But it has the extra-property that no other piece can capture it except Pawns. So Mamra is nearly invincible and it can be captured by Pawns only (not even by another Mamra).
Wuss - Piece invented by Dan Troyka. It moves like a queen but can not capture and must move when attacked.
Hydra icon represents a special multi-mutant. It starts out like knight, then it adopts successively the identity of each one of the following 5 Nachtmahr's crooked nightriders:

Diagonal Wide Crooked Nightrider: NN11. See a detailed description of its move here: Nachtmahr.
Straight Wide Crooked Nightrider: NN02. See a detailed description of its move here: Nachtmahr.
Quintessence: NN31. See a detailed description of its move here: Nachtmahr.
Diagonal Narrow Crooked Nightrider: NN33. See a detailed description of its move here: Nachtmahr.
Straight Narrow Crooked Nightrider: NN04. See a detailed description of its move here: Nachtmahr.

Oxybeles - Piece invented by Mats Winter. The Oxybeles moves like a king, one step in any direction, but it cannot capture in this way. Instead the Oxybeles, when it moves, has the power to sling a piece located behind itself to a forward square in the alignment direction. The slung piece, which can be of any colour, is located immediately behind the Oxybeles, in the opposite direction of the move. This piece can hit an enemy piece in the forward direction, provided that any intermediate squares are empty. If there is no enemy piece then the catapulted piece lands on the remotest square in a series of empty spaces. More details at Oxybeles Chess.

Secutor - Piece invented by Mats Winter. It is a bifurcation piece that must collide and deviate in order to capture. The Secutor slides on the orthogonals like a rook. It captures by colliding against any piece and then deviating to any of the two adjacent diagonals (in the prolonged movement direction). Thus to capture, the Secutor jumps directly to an enemy piece and lands on it, provided that any intermediate squares are empty. More details at Secutor Chess.

Cylindrical Bishop - Assuming that the board is joined at the outermost ranks ("a" and "h") as if it were a cylindrical board opened up, the Cylindrical Bishop can move, threaten, and attack across the edge because it 'wrap' to the other side.

Standard Pawn.

Berolina Pawn.

Scorpion Pawn - From Mats Winter's Scorpion Chess. The Scorpion has the additional moves of a knight, but only in two forward directions: east-north-east, and west-north-west. There are no additional capture moves.

The two oblique moves in the image (yellow circles) are the
Scorpions two extra movement possibilities.
It can only capture like a regular pawn.

Rules

After each move, pieces transform into another according to the following order:

1 King ---> Maoking ---> King
2 Queen ---> Sissa ---> Queen
3 Amazon ---> Squeen ---> Amazon
4 Archbishop-rider ---> Dragon ---> Archbishop-rider
5 Nightrider ---> Rose ---> Nightrider
6 Chancellor ---> Archbishop ---> Chancellor
7 Dancing Horse ---> Octopus ---> Dancing Horse
8 Dragon King ---> Dragon Horse ---> Dragon King
9 Knight ---> Knight-guard ---> Knight
10 Gryphon ---> Aanca ---> Gryphon
11 Crooked Rook ---> Crooked Bishop ---> Crooked Rook
12 Rook ---> Cylindrical Bishop ---> Rook
13 Knight/Wazir ---> Knight/Ferz ---> Knight/Wazir
14 Pao Vao ---> Cannon Pawn ---> Pao Vao
15 Chameleon ---> Swaper ---> Chameleon
16 Long Leaper ---> Archer ---> Long Leaper
17 Advancer ---> Withdrawer ---> Advancer
18 Immobilzer ---> Shield ---> Immobilizer
19 Mamra ---> Wuss ---> Mamra
20 Hydra (Knight) ---> NN11 ---> NN02 ---> NN31 ---> NN33 ---> NN04 ---> Hydra (Knight)
21 Oxybeles ---> Secutant ---> Oxybeles
22 Pawn ---> Berolina Pawn ---> Scorpion Pawn ---> Pawn

The CORNERING may be made by the king and any piece placed on the nearest corner to him; this piece on the corner may be even any dropped one. Both the king and the cornered piece should not have been moved previously.

If the king falls on the corners, of course, there is no need of any cornering.

If falls on b1/b8, then he will remain there and the piece on the nearest corner [a] will leap to c1/c8.

If falls on c1/c8, he will remain there and the piece on the nearest corner [a] will leap to d1/d8.

If falls on d1/d8 or e1/e8, the king may cornering with the piece placed at either corner by walking two steps towards it, and then the piece leaping the king to the adjacent square to him; exactly as in FIDE chess happens.

If falls on f1/f8, he will remain there and the piece on the nearest corner [h] will leap to e1/e8.

If falls on g1/g8, he will remain there and the piece on the nearest corner [h] will leap to f1/f8.

Dropping Performance

As a compensation for White's first move advantage, Blue will have the oportunity of making the drops before than White, making them thus:

1st: the piece on A8 in any turn between the 6 and 10 (including 6 and 10)
2nd: the piece on B8 in any turn between the 11 and 15 (including 11 and 15)
3rd: the piece on C8 in any turn between the 16 and 20 (including 16 and 20)
...
8th: the piece on H8 in any turn between the 41 and 45 (including 41 and 45)
9th: the piece on A7 in any turn between the 46 and 50 (including 46 and 50)
10th: the piece on B7 in any turn between the 51 and 55 (including 51 and 55)
And so on.

White must make his/her drops thus:

1st: the piece on A1 at any turn between 7 and 11 (including 7 and 11)
2nd: the piece on B1 at any turn between 12 and 16 (including 12 and 16)
3rd: the piece on C1 at any turn between 17 and 21 (including 17 and 21)
...
8th: the piece on H1 at any turn between 42 and 46 (including 42 and 46)
9th: the piece on A2 at any turn between 47 and 51 (including 47 and 51)
10th: the piece on B2 at any turn between 52 and 56 (including 52 and 56)
and so on.

That is, players have some flexibility to choose both the turn and the square in which the piece will be dropped. The square must be any unoccupied square of the player's first row or home row. But the dropping itself is MANDATORY; the extra pieces must come into the game NECESSARILY. This may be done at the same time that any one normal, regular move.

Whatever the type of pawn they must promote when reaching the opponent's home row or first row in this manner:

The first promoted pawn will be promoted by the last piece of the dropping order.

The second promoted pawn will be promoted by the penultimate piece of the dropping order.

And so on following the inverse order.

Notes