It is possible, but difficult, to wall jump this map with a partner using an air jump. If the first partner is running in midair at the right wall, the other mouse can "hold on to the ground" by running left. The left-running mouse should hold on the very end of the platform so his or her partner is as close to the wall as possible. To get closer, release the key momentarily. When ready, the left mouse then dashes at the wall. He or she will be flung into the wall with the force of the right mouse's pull; the right mouse is already close enough to the wall to run into it. This allows both mice to wall jump up and reach the cheese.
To get back down, a well-timed air jump out three-fourths of the way over the gap is necessary.
The shaman should build a ramp to help the mice get to the cheese. An airship is possible but would be difficult. Usage of the portals is generally avoided, since one mouse going in with the other trailing behind can prove disastrous.