I would rather see her find out more about him and him make an actual solid non murderous or clinically unhealthy attachment to another person.
There is more stuff going on with Stefan and Caroline I think at the moment. The little looks and saying 'I'd do it for you.' Etc I would rather see that move to possible ship status.
I think it would be great fun as friends for Enzo is good at understated sarcasm and Caroline is good at brutal come backs so it might have some laughs.
It will also be god as she will have a hard time killing the doppelgänger who looks like Stefan and Enzo doesn't have a problem killing anyone so there will need to be some quick thinking for Caroline if she wants to save both doppelgängers. If she can stop Enzo that is.