(Sounds like a fraternity.)
I present an epic Chess game that introduces new Major pieces with grandiose powers and new challenging tactical powerplay to overcome.

I - Set up
Though there are many more pieces to choose from some with powers more complexed than what one may be accustomed to, pieces of similar power are grouped into the original arrangement of FIDE chess, in order to add a familiar dimension from the original familiar game.
FIDE chess configuration: King/Queen, Bishop, Knight and Rook; pawns in +1 rank to conceal them at gamestart
CMT configuration: Queen group, Bishop group, Knight group and Rook group; pawn groups within +4 ranks to conceal and protect them during game start
(Diagrams have been sized down to fit thread parameters. Press ctrl key and scroll using the middle mouse button to enlarge text and image.)

Modes of movement: The following diagrams explain the algebraic graph notations that will serve as a legend to explain the powers of the pieces.

II – Pieces powers
a. pawn group: pawn, jack and gambit
Pieces’ moving power is different from capturing power. Movements move in an orthogonal (forward/backwards/sideways) line. Captures occur on a diagonal. Upon reaching the final rank, pieces in pawn groups may promote to a more powerful piece. All three pieces in pawn group may perform en pessant (with slight variations in rules for each piece).

b. Knight group: Knight, Hydra, Hippocampus and Pheonix***
***(Knight and Rook-type hybrid)
Pieces all primarily/exclusively perform a dissonant un-orthodox L-shape leaping maneuver to reach its final destination. None move primarily in a straight line, and none are susceptible to being blocked. Due to the nature of the L-Shape, these pieces’ movements cover squares that are mainly or exclusively the opposite color from the position they were previously in.

c. Bishop group: Bishop, Harpie (Roc), Stymphalion and Wizard
Due to their diagonal nature, pieces are color-bound to the colored square that they start on, with the exception of the Stymphalion, who has the lesser option to leave the colored square of its origin through a range-3 Orthogonal maneuver. (Though, most its power covers squares that are of its origin.)

d. Rook group: Rook, Champion, Helepolis and ***Phoenix
***(Knight and Rook-type Hybrid)
Pieces are used primarily/exclusively for its orthogonal property and, as such, are never color-bound. Any existing diagonal maneuver is minor or non-existent. Those ones that share the King’s rank can be castled with him: the Rook and Helepolis.

e. Queen group: Queens, Lion, Freyjan Giant and Titaness
The most potentially dangerous chessmen on the board, pieces primarily move orthogonally and diagonally, combining the directionality of the Rook and Bishop. Two in the group encompass Knight L-shape directionality as well. Pieces may be leaper or non-leaper, depending on the specific piece.