Well, I've just finished reading The Long Earth by Terry Pratchett and Stephen Baxter and what an excellent read it was!
It had a similar style to Peter F Hamilton's books I thought, though set in a very near future rather than the far future and with the usual Pratchett humour running throughout. I must try and read some more of Mr Baxter's books - I really enjoyed his alternative history novel Voyage but that's the only one of his I've come across. I've read virtually all Pratchett's.
A brief synopsis for those who haven't read it (but no major spoilers!): an anonymous posting on the internet provides instructions on how to built a "stepper" that enables the operator to travel (or "step") sideways to parallel Earths. This provides all manner of opportunities for colonisation of new worlds but without the need for space travel. The only problem is that you can only take what you can carry and for some reason no iron or steel can transfer with you (other metals can be transferred with no problem). The first few Earths you come to seem fairly similar to home (Datum Earth) but as you step farther away you discover more unusual worlds.
You could have a fun game with this idea. Set up 3 game boards (or even 5 if you can manage it) with identical underlying base terrain (ie. hills, rivers). All boards MUST be the same size. The centre board will be the home board with the objective for the battle, be this a certain individual who must be captured, a certain item to be seized etc. The board(s) either side will be a step or two away. The home board will have scatter terrain set up to include buildings, roads and other technological gubbins. The parallel boards can have completely different scatter terrain - perhaps one will be almost entirely wooded while another could be agricultural or maybe a rocky desert. Defenders on the home board will have access to vehicles and more powerful weapons (including steel parts). Attackers will be restricted to lighter weapons using ceramic or plastic parts that can be transported between worlds when they step.
Special stepping rule - rather than a normal move, a figure can make a "step" move to transfer to a parallel earth. This takes up the entire turn during which they can perform no other action (it takes full concentration to activate the stepper and to recover from the "step sickness" when you arrive). The procedure when stepping is as follows:
1) Player 1 declares that they are stepping and which direction this will be (parallel game boards are East or West of the home board, these directions should be identified clearly before the game starts!). They are not allowed to measure to see where they will appear on the target board - they just have to hope that they have estimated correctly!
2) Player 2 (or umpire if you have one) measures the exact position of the figure (use XY co-ordinates in centimetres, inches or whatever) and plots this point on the destination board.
3) If the space is empty of fixed objects (trees, walls, immobile vehicles etc.), Player 1's figure can be placed here. Allow a little flexibility, say 1 - 2 centimetres to allow for the stepper to shuffle around a couple of paces to find a clear space. Note that they can step into buildings as long as the floor level is equal or below their current ground level. If (even after the 1-2cm shuffle) the space is occupied by something, Player 1 cannot step but can still carry out some actions on their curent game board. They may continue with half their normal amount of actions, eg. do a half move/fire half the usual number of times/either move or fire but not both - exactly what is possible will depend upon what rules set you are using but make sure that all players understand this before the game starts!
4) If the player has succesfully stepped, they can do nothing for the remainder of the turn exept crouch down and throw up due to step sickness. Note that this may put them into cover depending upon the surrounding scenery. Nearby enemy troops who have not yet acted this turn will need to make an initiative or quality test of some sort to see if they can react to this sudden appearance. Plus or minus modifiers may be apropriate depending upon whether they facing towards or away from the stepper. Again, make sure you have agreed these before the game starts!
5) If a stepper has emerged above ground level, determine whether falling damage is required - or perhaps they've fallen from a bridge into a river? You can have all sorts of fun here...
The real challenge will be in the tactics to use bearing in mind that a stepper can simply swap worlds to get through building walls or past defensive lines. Defences might have to be built multi-storey or underground so that anyone stepping still has to fight their way up or down to each their target.
A few extra things that could add more fun:
Does either side include a natural stepper who does not get step sickness - additional points cost but they get a half-action when they emerge (the same as someone who fails a step).
Perhaps each player gets a chance to change a single piece of the underlying ground terrain - the river curves left here, not right, or there is an extra hill.
Does one of the parallel worlds have dangerous features such as dinosaurs or a toxic environment?
What happens when your unit ends up out of coherency because some of them are on another world!
It would be a pretty big game to run (and possibly very confusing) but would provide some unique challenges!