Defied: A new character is introduced who has similar powers to Drake and a similar backstory, but has a very different personality.
Discussed: Drake's nerdy friend calls Missy-Sue a blatant Copycat Sue to her face.
Conversed: Fred writes fanfiction about Drake, and is about to introduce an OC like this when Jim explains why it's a bad idea.
Missy-Sue is an Opposite-Sex Clone created by the Big Bad, given false memories similar to Drake's in order to study how he thinks. She breaks loose, meets up with the actual hero, and goes insane when she discoveres that her entire life is a lie.
Drake's Sueish doppelganger is actually a Humanoid Abomination that was specifically designed by Emperor Evulz to be exactly like him for the purpose of eventually replacing him in the heroes' team so that they can no longer foil his Evil Plans. The copy eventually succeeds, but the other heroes catch on to the fact that "Drake" hasn't done any real hero-ing as of late, exile/murder the clone, and develop a paranoid fear that any one of them could be replaced at any moment, causing Fantastic Racism towards all clones and eventually causing them to kill each other over even the ''slightest' Out-of-Character Moment out of fear that they're Evulz's new clone mole. With the heroes infighting, nobody is left to oppose the bad guy.
The resemblance is so uncanny that characters in-universe pick up on it; as a result, they mock him/her, pointing out that s/he can assert originality all s/he wants, but the fact remains that the character's just a cheap knock-off, a joke.
Just because they are similar to one another, doesn't mean they get along. Both have a bad temper and are very stubborn or they both are Insufferable Geniuses who constantly try to one-up one another. This results in a lot of fighting amongst the two.
As above, except that she ends up turning on the Big Bad and joining the heroes for good, eventually developing into a distinct character.
Sure, they have arguments and fight every once in a while, but they're still good friends or perhaps lovers.
Plotted A Good Waste: Missy-Sue is introduced as being very similar to Drake only more powerful. Rather than giving Drake the chance to ponder the implications of this and working up the drive to try and surpass Missy-Sue one day through hard work or clever tactics, he (or another supporting character) falls in love with Missy-Sue and the rest of the fic is a rather standard Romantic Comedy.
Bob: "Back to Copy Cat Sue" Rob: "Return to the super awesome Copy Cat Sue main page, bro!" Bob: "Wait-I just said that..."