1) Let's try a different chord structure. Rather than layering the chord in the "root - fifth" format, let's try harmonizing the root directly and solely with it's 3rd.
2) From here, it's very simple to add other harmony other than a perfect 5th. In part two, we see an added 9th (quite simply, an A minor scale starting from the 10th fret of the B string, stacked on top of the original diads and ascending one scale position at a time).
3) Lastly, we throw in the 7th harmony. From the vantage point of the first chord, it'll be an A minor scale, ascending from the 7th fret on the high E string, stacked on top of the original diad and added 7th.