I think that the Sanders Sides might represent more than each has told.
Okay, so we know that the sides can represent more than just their official role. Logan also represents reason, knowledge, and realistic expectation. Patton also represent emotions, childlike wonder, and over controlling yourself. Roman also represents passion, ego, femininity, and masculinity. We haven't seen a lot of Remus, and have no official things that he represents besides intrusive thoughts, but we can surmise based on his personality and entrance he also represents dark thoughts (such as ones induced by depression), disturbing thoughts (which are very different from intrusive thoughts), and impulsivity. Janus represents deceit, denial, self-preservation, and selfishness. As for Virgil, he represents anxiety, but he also represents shame, apprehension, introversion, pessimism, paranoia, fear (to some extent), foresight, caution, anticipation, motivation (slightly, but this is more by proxy of him representing anxiety), and satisfaction. Now, that last one may not seem accurate, but here's a quote from Accepting Anxiety Part 2 from Patton: "ALSO, YOU'RE THAT FEELING OF TINGLINESS AFTER ACHIEVING SOMETHING HE DIDN'T THINK WAS POSSIBLE!" That feeling is known as satisfaction. However, satisfaction doesn't seem to go along with the other things he represents, which are all before the event things, while this is a post event feeling. So perhaps he represents more similar things, and perhaps the other sides also have more to them. Let's take another look.
Logan first. Now, if we inspect his behavior throughout the show, we notice something: He seems to get annoyed easily. He also gets angry rather easily. Some would say this signifies that he's being influenced by the orange side, and that the orange side is Anger/Wrath, but I have my own theories about that. I think that this may mean Logan may also represent Anger and Annoyance, two things that would go right along with Logan's personality, and his habit of being ignored over the need to be polite.
Next, Roman. Now, for Roman, it's a bit tricky, however, if we look through everything, including how he acts towards the Dark Sides, we begin to realize something: He seems to decry and defame anybody who is different, suggest a different idea, or who is criminalized by the world. Therefore, he may also represent Bias/Prejudice and Societal Conformity.
Third, Patton. Now, Patton is extremely difficult, but after some searching, verifying, and double-checking, I noticed that Patton's default is to try to convince the other sides that his way is most important, often going to Roman first, then Logan, then the others, in no particular order. Therefore, it could be that our dear daddy Patton also represents Manipulation. However, the reason he hasn't taken total control of them all by now? One, he is likely repressing that part of him in favor of being "nice", and two, Patton is canonically an indecisive mess. With that in mind, we can accurately guess that Patton likely also represents Indecision.
Fourth, Remus. Now, Remus' is a little bit obvious, he essentially says it right up front with the 'cut out all the juicy stuff' comment. Remus is Honesty. And as for the other, it may seem odd, or like I'm reaching, but hear me out. Remus makes a lot of comment about religion, especially on the way of innocence, the losing if it, as well as biblical events that were meant to teach a lesson. Therefore, it is possible that Remus may be Wisdom.
Now for Janus. In SvS Redux he didn't use lies at all near the end, relying instead in harsh truths, ones that Thomas maybe would've preferred to have been kept in denial about, so clearly he didn't care about or even consider his purpose as Deceit. Plus, Thomas wasn't even lying here, so Janus shouldn't have even been summoned. Some would claim that Thomas was in denial, and that's enough, but we have seen that the state of simply being in denial is not enough to summon him, or he would've been summoned three or four thousand times in the first season. You have to actively lie to summon him, and Thomas wasn't actively lying. Additionally, he was summoned in DWIT, when Thomas clearly wasn't intending to lie, and objecting to it in the first place. You know what he was feeling both times? Guilt. So perhaps he represents Guilt, which, while similar to his normal things, is also very separate from them. Now, in addition, we notice that Janus only attacks or uses sarcasm as a defense mechanism. Additionally, his whole purpose throughout the show has been "Protect Thomas by keeping him in denial," but then it became "Protect Thomas by helping him face his inner demons," as seen by the fact that he revealed Remus and allowed them to defeat him when he could've just let Remus keep festering, which would've actually benefited Janus, but not Thomas. So perhaps Janus represents Protectiveness as well, even protectiveness towards oneself.
Now, with this in mind, the realm for what Orange could be suddenly got a lot smaller. It has to be something that could be a dichotomy of Logan while not being an emotion (as none of the sides are an emotion, with the exception of Virgil). Additionally, it needs to leave room for him to also represent things that are not directly related to what he is. Now what is he? I can't say, though I do have my theories.