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Several weeks ago someone posted a discussion on /tg/ about playing 40k in 4 dimensions and it got me thinking. Below is a three-quarters-baked team based scenario with a multi-dimension spin. Please commence spear chucking:

Table Set Up
Centuries ago a warp anomaly created duplicates of a world, all existing in the same location, albeit shifted to a slightly different “plane” of the warp. This is depicted on the table top by having multiple tables set up with similar terrain setups. Each table represents a version of the world. The the set up does not have to be identical, but, for example, there would be a forest of similar size in the same location on each table. In the time that the duplicates have existed, different histories have developed and a forest on one world would likely be different from one world to another.

Objective
Each table is assigned 5 objectives, to be placed alternately by the players playing at the table. (Roll off for first placement.)

Deployment
The two teams are divided into parings and each paring is assigned a table. A single deployment type is rolled for all parings and a single roll for first deployment is made. The team that ends up with first deployment decides as a as a group which zone to take, effective on all tables. Each table then deploys their forces as normal. Attempts to seize the initiative are done individually on each table.

Victory Conditions
Before rolling for steal the initiative, roll a d3 for each objective. This determines the victory points awarded for controlling the objective at the end of the game.

1 point is awarded for the first blood on each table
1 point is awarded for each warlord on the other team slain
1 point is awarded one each table for having at least one line breaking unit

Special Rules
Shifting planes: During a units movement phase, the unit my attempt to shift planes instead of moving. To do so, roll as if moving through difficult terrain attempting descend/ascend levels of a ruin. A roll of 3 or better allows for shifting one table, a 6 allows for shifting 2 tables. All units roll 2 dice for this check; move through terrain has no effect on this roll. Any doubles rolled result in the unit suffering a randomly assigned perils of the warp wound, as a model is lost to the warp during the transit.

Each table is assigned a letter: A, B, C, etc. Shifting can only be made in one direction A->B->C->etc. The last table then loops around back to table A. A successfully shifting unit arrives on their new table in the exact location they were on their own table. When they arrive they are treated as coming from in from reserves (count as moving, and cannot make assaults).

Fliers and swooping FMC cannot attempt to shift planes.

If a unit successfully shifts from or into terrain, each model must take a dangerous terrain test.

Vehicles may attempt to shift, but only if they are on open ground. Vehicles must still take a dangerous terrain test after shifting. An immobilized vehicle also may attempt to shift and still take a dangerous terrain test with a failure resulting in the vehicles becoming a wreck. War gear that effects dangerous terrain tests in any way have no effect on this test.

Psykers may expend a warp charge attempt to better navigate his unit across planes and roll three dice, choosing the highest, to test for shifting. On a roll of triples, though, the unit suffers d3 perils.

I think it would be cool to watch, maybe a little confusing to play, but still cool nonetheless.

I am always up for different and unique mission types. I think this could be a great deal of fun. I might consider putting a rule in where the unit might shift a level against their will. (this is the warp after all) something like in the movement phase roll for each unit that isnt intending to shift. On a 6 reroll, if you get a 5+ on the reroll you are forcefully shifted a plane. Just an idea.

...You do know the fourth dimension is technically time, right?

This seems unnecessarily complex and doesn't really add a lot to the game...

Interesting. It reminds me a bit of 3 dimensional chess.

Shouldn't crypteks and haemonculi also be able to phase, since their respective races also have some form of dimensional manipulation?