Second Dog?

I was considering getting another dog to keep my Lexi (1 1/2 year old female Maltese) company. There was a 16 month old female Maltese up for adoption in my area so I packed up Lexi and off we went to meet her. Lexi totally ignored her even when she was 2 inches away from her face. When the other dog came near me, Lexi nipped at her. I decided not to adopt her because there was a waiting list to get her and I didn't think it would be fair to her. Since dogs are pack animals, I thought Lexi would like the companionship. My question is: If she is this possessive of me, should I be considering another pet? If yes, is there a type of dog that she would accept more readily and what is the best way to get them to accept each other?

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