When you sign in to CircleCI, you do so via OAuth with the selected VCS provider (example: Github). From there, you can add additional account integrations (example: BitBucket) on your account's page here: https://circleci.com/account
If you run into a situation where you have linked an account previously and are trying to connect it to another account you will see this error:
We encountered a problem adding your identity to CircleCI... The identity provided by your VCS service is already associated with a different account. Please try logging in using that account or contact us for further help.
If you receive this error, you may contact Support at the link below and we can unlink the accounts so they may be rejoined as you wish.