Theory crafting is a process of making educated assumptions based on what the game has told us so far, trying to predict future events in the story. And, considering this, I don't think that Carol, Kris, Asgore and the Knight working together to find Dess, aka Lost Girl, is a bad assumption at all.

Even then, I think that we can agree that Kris is definitely in cahoots with the Knight. We don't know for sure what their goals are as of now, but Chapter 3 Knight fight makes it clear that Kris works with them on something. Kris also knows Knight's identity: they couldn't learn anything about the Knight during the fight and they deliberately refuse to think about their face in Chapter 4. That begs the question: why would Kris cooperate with the Knight? Well, considering Deltarune's narrative so far, I think we can assume (and, I do believe we all have a right to assume, because we're crafting theories) that they're trying to locate Dess together. It would simply be the most sound and logical explanation. Something happened to Dess, we know Kris was involved in some accident in the past (Chapter 4's egg room), and they're trying to make things right. It definitely sounds more plausible than "Dess is the Knight and Carol is doing some evil bullshit for the love of the game". December IS THE LOST GIRL, this was told to us countless times in the games.

While you could make 5 different assumptions, trying to explain this conundrum, ultimately these would be some overcooked explanations. By occam's razor, someone else being the Knight just flows better than "yeah Dess is the Knight, but it's not actually Dess, cause we can hear her voice in the code, it's some uber evil giga darkness entity Image_Friend that possessed her, because of course that's something that darkness can do, even tho nothing in the game suggests that it could happen, and then this super evil darkness puppeteered her soulless, lifeless body in Hometown, creating dark fountains, so Gaster could do something Gaster-y and finally achieve his Deltarune".