Basic Trope: A deeply flawed character that still somehow has the plot bias of a Mary Sue.
Straight: Alice is foul-tempered, lazy, and repeatedly described as being very ugly. Despite this, she's still the center of attention and her flaws neither fade through Character Development nor have any meaningful effect outside of making her more "relatable".
Exaggerated: Alice is completely incompetent, has an incredibly abrasive personality, and is so ugly that looking at her directly can cause brain damage. Even though nobody should want anything to do with her, she has three romantic subplots, an archnemesis who wants to kill her for some vaguely-defined reason, and a small army of allies working to prevent this from coming to pass.
Or alternatively, Alice (if you think about it) is perfect in every way. Yet she is portrayed as a bad guy and is supposed to be hated by everyone in-universe and by the audience.
The character turns out to have been Suetiful All Along and was deliberately hiding her awesomeness in order to avoid the revulsion typically caused by Mary Sue, but by doing so accidentally invoked Anti-Sue.
Everyone is just pretending to be her friend. So they could get revenge on her without her suspecting a thing.
They were pretending to be her friends. But they're actually starting to like her.
Parodied: When Alice leaves to go to the bathroom, there's a massive shock as everybody suddenly realises that they hate just being near her and that she should probably seek therapy. Then she comes back and, once again, even the girls are inexplicably proposing her.
Zig-Zagged: Alice, who is narrating the story, describes herself as unlikeable even though she has dozens of admirers. However, it turns out that Alice is an Unreliable Narrator whose modesty causes her see flaws where none exist — in reality, she's a straight-up Mary Sue. However, because she thinks she's an Anti-Sue, she begins to act like one. Her admirers remain, though, because they were only ever interested in her money. When she discovers this she abandons her false friends, shapes up, and joins a group of admirers who worship her for the Mary Sue she really is.
Averted: Alice is a balanced character whose flaws fade naturally through Character Development and whose presence doesn't completely dominate the story.
"wtf u stupid preps why do u think that my oc is a mary sue just cuz she's pretty??? well fine then shes so ugly she makes kids cry are u happy now?!?!"
Before story is even written, the author decides: "I better make the character ugly...that oughta prove that even ugly people can find friends..."
Lampshaded: "Uh, Bob? About your not-girlfriend... It's true that there's No Accounting for Taste, but I think this may be pushing it a little..."
Invoked: Alice is a Purity Sue, is aware of that fact, and — like so many fanfic authors — doesn't understand how Sues work and tries to avoid it by being an Anti-Sue.
Defied: Alice is hideous, cruel, selfish, and mean; therefore, she is a Chew Toy and Butt Monkey.
Discussed: "You know, from a logical standpoint, Alice really is nowhere near as special as we all make her out to be."
Conversed: "Have you ever noticed how the more flawed a character is, the less likely those flaws are to actually mean something?"
Deconstructed: Since everybody (with some obligatory exceptions) loves and cares about Alice unconditionally, she is completely free to do whatever she likes without fear of social stigma, and becomes the absolute worst kind of monster — even though she's whiny, pointlessly selfish, needlessly cruel, and can't be left unattended for 10 minutes lest she find some way to injure herself, you can't help but love her.
Reconstructed: Even though Alice is a generally nasty piece of work with few redeeming qualities, everybody loves her and wants the best for her — however, she's on thin ice (metaphorically speaking) as far as many of her friends are concerned, and after a while her actions start to drive away people she cares about, causing her to realize just how horrible she is. Character Development ensues.
Plotted A Perfectly Good Waste:
Alice is ugly, nasty, and cruel, but she has the entire student body at Trope T. Trope High School wrapped around her little finger. This is because she's a Manipulative Bitch and can blackmail her peers into giving her the Mary Sue treatment. Unfortunately, Alice is fully aware that her treatment isn't genuine, and (optional) ultimately pulls a Heel-Face Turn and works to earn the reputation she created for herself.
Alternately: Alice is mean, cruel, and ugly, but keeps up The Masquerade of Mary Sue qualities so well that her peers are fooled. But her disguise eventually breaks and her popularity goes down the drain.
Alternately: (again) Alice is ugly, mean, and cruel, but she makes a Deal with the Devil to become the most popular girl in her school regardless.