I like the way this site puts it down:
https://www.easydamus.com/alignment.html
There is some leeway in interpreting each alignment, say "neutral", which can both represent a guy with no strong convictions, just doing what seems good to get by, and a guy
who gets all philosophical about maintaining balance, preaching moderation and being overtly critical of anything extreme.
When bunched with another alignment, I like to interpret "neutral" as being a blank which dials the other half of the character to 120%.
Similarly, an "evil" character will justify a whole bunch of actions, from the moronic biowarean trope of cackling and being mean to people for no reason, to simply always putting one's self interest first.
I think this variety of interpretation is necessary in the context of building a party. A Chaotic Neutral and a Lawful Neutral would find very little in common and this should serve
as a constant source of interpersonal tension. How to make them work together nonetheless? It's a good breeding ground for some comedy, but you don't always want that.
The logical and easy choice is to confront them with an even greater, extreme Evil, one that would threaten the identity of both of them on a fundamental level.
An interesting mental exercise would be if same could be achieved with an extreme Good. Perhaps the LN character will be offended by the perceived lack of efficiency
and promotion of mediocrity and find some common ground with the turbo-individualistic CN?
Now, the original question was about Chaotic Evil, which I think should be about as obnoxious a thing to fit in a party as Lawful Good.
My preferred approach is to have them both as "necessary evils", with plenty of personal tension due to the extreme nature of such characters,
basically these are guys everyone tiptoes around and grits their teeth because they are needed for a specific purpose, because they either set the tone for the entire ensemble,
or become that guy who sits alone by the campfire.
Of course, fantasy tropes being fantasy tropes, a LG questing paladin is always a tad easier to justify in a party than the CE guy.
What interest would they have in pursuing a noble adventure other than being forced to? Or perhaps just pursuing an own agenda which at the moment aligns with the rest of the party.