The true personality may not be evident in a rescue environment.
Don’t pass over a dog that may not be reaching out for your attention.
Plan to meet at a neutral location to avoid territory issues from either the new dog or your existing dog.
Never let two dogs greet each other face to face in the beginning. Always walk them one in front of the other to release the initial excitement about the meeting. Keep the initial visit well supervised to avoid issues.
Visiting more than once with the same dog before taking it home makes everyone more comfortable with the match.
Consult an adoption coordinator to get their thoughts on whether or not your choice has a good chance of working. Trust their experienced input as they would personally know the dog in which you are interested.