Then it hit me, I can.
I need multiple files layered one on top of each other. To do this, I used the dual-extruders available on the machine to thin the layers out a bit, but the technique is possible with single extrusion as well.
Basically you need to load File 1 and switch to different colours when it finished before loading file 2 (I've done 8 colours so far). (After each file finishes, it is important to keep the platform of the machine heated so that nothing comes loose.)
In total, I used Sketchup, ReplicatorG, NetFabb Basic, Adobe Illustrator, thingiverse and Meshlab to get everything done.
I've attached several photos of things I've done using this technique in the last few weeks.
Note, the 3D part of the stairwell was taken from Thingiverse Item 18290 - PrettySmallThings.