The absolute most we use up to is tertiary and we try to avoid even that. Anything else was deemed unnecessary as it's not that important to the overall audience nor does it improve anything to try to glorify those roles. After tertiary we use simply antagonist/villain or minor antagonist/villains.
It's been this way for a while now and it was a headache before because it's abusing the villain scale to the point it got ridiculous so no I highly doubt any admin here will agree to change these guidelines.
In fact, the Villainy Scale has been simplified to Main, Major (secondary can be used if there are only two villains), Minor, and One-Shot.
There are still some articles which use the older—annoying—scale, but they will be addressed when the Cleanup reaches that phase, although we can change them as we find them on pages needed editing in the nonce.
You don't need to stop using all of these. There is merely a new scale: Main/Primary - Secondary/major - minor. Anti-villain, anti-hero etc can still be used. It is only that after secondary, there is no need to still continue with tertiary etc. as they are mostly not important enough to be differentiated.
For example, the entire Crew of the Flying Dutchman can be summed up as "minor villains" or simply "are villains in the movie..." They are not really fleshed out as characters, they merely serve as henchman and are present in the background or during some conversations with Davy Jones.
EDIT: By the way also don't use "true" main/secondary/etc. antagonist" or "main, later secondary antagonist" anymore.