The question of how many satellites it would take to accurately map the spatial distribution of ionospheric outflow is addressed in this study. Given an outflow spatial map, this image is then reconstructed from a limited number virtual satellite pass extractions from the original values. An assessment is conducted of the goodness of fit as a function of number of satellites in the reconstruction, placement of the satellite trajectories relative to the polar cap and auroral oval, season and universal time (i.e., dipole tilt relative to the Sun), geomagnetic activity level, and interpolation technique. It is found that the accuracy of the reconstructions increases sharply from one to a few satellites, but then improves only marginally with additional spacecraft beyond ~4. Increased dwell time of the satellite trajectories in the auroral zone improves the reconstruction, therefore a high-but-not-exactly-polar orbit is most effective for this task. Local time coverage is also an important factor, shifting the auroral zone to different locations relative to the virtual satellite orbit paths. The expansion and contraction of the polar cap and auroral zone with geomagnetic activity influences the coverage of the key outflow regions, with different optimal orbit configurations for each level of activity. Finally, it is found that reconstructing each magnetic latitude band individually produces a better fit to the original image than 2-D image reconstruction method (e.g., triangulation). A high-latitude, high-altitude constellation mission concept is presented that achieves acceptably accurate outflow reconstructions.