One thing that I absolutely loved about the Dr. Aeon SF is that it gave the Goldbrickers a much needed backstory and an AWESOME one at that! There was a lot of room for creativity using the Goldbrickers because they really had no definitive story of their own. King Midas had never even been conceptualized so it gave the devs the ability to capitalize on that and turn him into a unique AV, along with the other AVs as well.
Following that same principle, I think a new SF or TF should revolve around other groups of enemies who have very little in-game story, or simply enemies you rarely see in SFs/TFs but already exist within the game. While an entirely NEW group of enemies would be cool to see, why not capitalize on what already exists that hasn't been utilized to its full potential?
So.. while I'm unsure of WHO specifically should issue any new SF/TFs I would love to see the following enemy groups:
1. Trolls! Technically speaking, the Trolls don't even have a definitive AV! Their leader "Adda" is listed simply as an Elite Boss on the homecoming wiki. I think that alone leavs a ton of room for new original ideas within the Troll ranks and further expanding the story behind Superadine!
2. Wyvern! Again, this is a group of enemies who have no AV of their own and are RARELY fought. While I'm unsure of what a Wyvern storyline would consist of, their in-game description is as follows: "Wyvern is a private agency dedicated to eliminating problems Freedom Corps hasn't or won't deal with." Which I think could make for an interesting Vigilante/Rogue themed SF/TF.
3. The Family! While there is a pretty good amount of in-game story revolving around the family that can be played through regular story missions, I think it would be neat to see a mafia sort of themed SF/TF! Another group lacking a named AV, I think there's a lot of room for expansion here.
4. The Infected! An enemy group that once only existed in Mercy Island but now can be fought in Atlas as well. This enemy group has virtually NO backstory. They have ONE named boss who is fought in a low level story arc from "Doctor Creed". Clearly a ton of room for creative design within this group.
5. Prisoners! Only seen in the redside tutorial and Brickstown, another enemy group rarely fought and virtually non-existent in any missions. I absolutely LOVE the designs of the Prisoner bosses. This would make for a cool "Prison Break" style themed SF/TF focused around the Zig, perhaps involving floors underground where much more dangerous Prisoners are held and have started rioting. I believe something like this also leaves room for other enemy groups to be involved as well.
Those are just some ideas I quickly typed up and there are many other enemy groups who have little to no story that could be used as well.