Okay, let us say we do, do that. We have a Mid-Faction tier. If people already think having Minor and Majors are already a problem because "many stories die" be it they die in the minor faction itself due to lack of activity/interest/whatever reason or in the Major faction where maybe the faction as a whole isn't the ideal place for their type of story. Having a mid-faction tier is going to segregate things even more, including the writer base.
If you're story does not align with the major faction you are in, that is OKAY. There may be some liked minded people who are in tune with YOUR story and with those like-minded people, that can branch off from that major faction and create a minor and build off to become a major. Perfect example would be the GA and the THR (royal naboo at the time). Or even the TSO and TSC.
No one is stopping anybody from becoming a major, except poor attitude and lack of involvement/activity.
You don't have to apply to be a minor faction. You can be a completely brand new writer and make a minor faction. You can still write, rp on planets, have stories, include major factions in your story. Heck, you can even go to a major faction and be like "I would love for my minor faction to collab and be apart of your major faction, if it aligns with what you guys are doing" or "I would like to keep my minor faction a thing, but somehow work to intertwine our stories together." To help support each other for activity and get more of your story out there and garner more support. Building up positive relationships with other writers/characters around. See what comes out of it.
If this is all about "my story dies", I know it's a hard to swallow pill: But your story dies, when you want it to or let it die.
This is a hobby at the end of the day and if you're not having fun writing your own story... then I suggest taking a break or re-evaluate the situation and try something new with the story/group/attitude/whatever you want to call it. It is called a "plot-twist", "pivoting", "filler episodes" for a reason. A simple question: "how can I make the story that I am writing now, more appealing while keeping the same tone, bring more people in?"
If it's a personal thing, such as poor attitude/difficult to work with and not being open-minded... once again: Chaos is all about collaboration, cooperation, and story-telling. Don't get me wrong, you can have poor attitude and still write your own stories, people may be still be interested in those stories and want to be included, but do not be surprise if collaboration or cooperation from other minors or major factions don't come hand in hand.
And if people already think going from minor to major is still a struggle, adding a mid-tier is going to make it even harder and worse. Even more stories will be "lost".