IT WOULD TAKE A WHILE he is still pretty obsessed with terezi rn, though he is in the process of attempting to get over it and start over with her now she's back
since when he didn't try to get over it while she was still here they ended up having a humungous fight which ended with them not on speaking terms
and karkat prefers having terezi as a friend to not having terezi as anything at all
also he has a crush on nill from dogs but she is seventeen and thinks of him like a little brother so that one is hopeless from the very beginning whoops

but it is definitely possible!!
karkat just needs to stop blinkering himself to the fact that wow nepeta is actually pretty badass
though it is also likely that the relationship will not be as good a one as nepeta will probably expect considering it's KARKAT and he is horrible at redrom