Before revision:  The center region, far from the overlap ends, has a constant motor density as one would na\"ively expect.
After revision:  Overlap motor density profiles and motor trajectories resemble experimental measurements. The phase diagram of the model is similar to the single-filament case for low switching rate, while for high switching rate we find a new low density-high density-low density-high density phase. The overlap center region, far from the overlap ends, has a constant motor density as one would na\"ively expect.