We have a rescue dog who came w/"mild" SA. Fortunately, my husband and I are retired and absolutely devoted to our dog.

No, adding another dog does not usually help.
Our behaviorist gave us the "alone-time" protocol [in short increments--mins at a time] to follow.

Also, we would NEVER leave our dog alone in a crate for more than a few minutes.....

We take our dog w/us, or one of us stays home w/her, or if we both have to go and cannot take her along, we hire a sitter.
Our dog also has issues w/other dogs, andso we cannot drop her off at a daytime dog care facility

It is an ongoing project overcoming this problem. It has drastically changed our lifestyle.