Variable Phase Order?!

So I was listening to an older podcast today from Ludology about game structure and it got me thinking about playing with the core structure of a game during play, and how that could really be accomplished.

Imagine if you will a game with multiple phases, that at the start of the game are in a specific order, but during the game the order of the phases can shift. So, lets say we have a hand management phase, a board manipulation phase, a combat resolution phase, and a cleanup phase. And that they start the game in that order. We have a handy card reminder for each phase that says what happens during each phase and we have a marker to indicate which phase we are actually on. And we have a marker that indicates which "direction" the sequence of phases will move. And during each phase, there is some means of altering the other phases in some way:

Hand Management Phase

At the start of the game, it consists of two actions. Every player draws a card, and may play a card. The card may shift the phase order, replace/augment a phase card, be placed in front of the player to grant them some kind of special ability, modify the board, or anything else really.

Board Manipulation Phase

This could start as an area control mechanic/worker placement, where if you are in control of a given area it allows you to perform an action. These could be almost anything, but some at least should allow further card play.

Combat Phase

Maybe after a significant enough victory, a player can flip the direction that play proceeds through the phases? i.e. if the current phase order was Hand Management, Board Manipulation, Combat, Cleanup, they could flip it to Cleanup, Combat, Board Manipulation, Hand Management? And since they were in the Combat phase, they would effectively prevent the cleanup phase from taking place. Or maybe this choice could be made by a player who loses a conflict by a significant enough margin?

Cleanup Phase

Restoring resources to players, changing the first player, score victory points (VP), whatever. This is the one phase I'm not sure should have a phase altering system, but maybe if there is a VP system this could be how this is manipulated. Say the player with the lowest VP at the end of the cleanup phase can switch the position of any two phases.

In any case, just a crazy idea I'm working through at the moment...