Accounts have a many to many relationship with contacts out of the box. I already have accounts imported. When importing contacts with CSV, I can map to Account ID only once.
What do I need to do to associate another account with the contact using import?
Hi, welcome to the Community! 
It’s… complicated.
But the short version is, only exceptionally, a Contact can belong to several accounts, and the UI won’t be too helpful in helping you manage that.
But it is possible. And possibly, your import is already doing what you want, but you’re not seeing the results form the Contact’s detail view; but maybe you can see them from the Account’s contacts-subpanel.