Hi vmsyvert,
Since I never owned the black skirt before, I can't advice from the experience but generally most Tetras would do better in bigger school. However there is only so much room for your 10G tank. But I think it is possible to add 2 or 3 more and sometime the aggression would spread out. However it is almost necessary to quarantine the new fish so your fish you already have will not catch any dieseace the new fish may have. I do not know if you have quarantine tank or hospital tank.
Also fish is like a people sometime some fish is more mean than other even they are same specie. Sometime their temperament is different by the way they grew or kept or even genetically.
So it may help to get few more but nothing is gurantee. For now I would say do some water change and rearrange the decoration maybe add more plants and decoration so there are more hiding escape spot for the fish getting picked on. If adding more stuff do not help then, I think it would be good idea to get few more.
Hopefully you get more advice from someone who has kept these fish.