Since I have made a theory on each of the authorities origin, purposes and abilities in my last blog, I should focuse on the Authority of Envy this time, specifically on its abilities. Here it goes.
Jealousy Inducement: Like the Authority of Wrath, Maybe one of the Authority of Envy's possible abilities is the the ability to induce massive amounts of jealousy on someone, to a point were the victim would want to kill and turn against the people they were made to be jealous of.
Identity/Ability theift and usage: Like the Authority of Gluttony, Maybe one of the possible abilities is to steal any aspect of your victim ( name, memory, relationships, abilities, appearrence, intellegence, etc.) and use it to your advantage.
Destruction Inducement: Maybe to add a sense of irony to the Authority of Envy, It could be that " now matter how much you are jealous of someone, you will never have what they do" and so causing destruction upon the person you are jealous of, you be the closest you will be to fullfilling your jealousy...kinda like of a " if i can't have it, no one can!" type of theme to it. (Kinda like the Authority of Acedia- can destroy all things using the forces of gravity.)
Identity Manipulation: Like the Authority of Vainglory, Maybe the Authority of envy can change any aspect to the user's self (either it could be their appearence, ability, situation, lifestyle, intellegence, experience, etc.) But since this is over powered, maybe the draw back is, is that the more you use this, the lesser you are truely yourself or maybe you go crazier each time you use it. Better yet maybe the draw back is that, you can only change your identity or situation that is similar to others. (You can't make your original identity, you can only at the most, mix other's identity aspects to yourself)
Life Destruction:Maybe the Authority of Envy can ruin someones life automatically. Here is my evidence according to this wiki
"Minerva mentioned during the Witch's Tea Party that Satella might direct her jealousy toward her if she stepped in between her and Subaru, suggesting that it's something that affects people remotely"
So maybe Satella can project her jealousy remotely onto her target and ruin their lives.
- note: I did write this theory on Satella's page, but I felt it would've gotten more feedback on my blog page instead, so I decided to post it here.