It may or may not work. Hard to know until you try it. Could you "borrow' a compatible dog to see if it helps? My first separation anxiety boy wasn't any better with company, but then the company was a bitch who didn't like him! My second one was an "only child", but we managed to get past the problem. Both of these were adopted as adults. The pups I raised didn't have any issues.
My first Basenji (male) had terrible separation anxiety. He hated being crated, and would howl and cry if left alone, even for a few moments. When a good friend became terminally ill and asked if I would take care of his female basenji and give her a home, the separation anxiety disappeared. The two of them were fine together. I could leave them together, curled up on the sofa, and never heard another peep from him.
My first boy was so anxious, we had him alone for 8 months. He was a mess! He pooped, peed and threw up in his kennel on the daily. We got him his sister and it all stopped! After that we have been a 2-3 basenji household. Life is much better with more basenjis.
We got our first basenji 23 years ago, a pet. I loved her dearly (I was 40 and had wanted one since second grade!).
I don't think she actually had separation anxiety, I called it 'Play with MEEEEE!' syndrome. I was home all day, as were our kids, and she just did things constantly that got our attention if we weren't paying attention to her. Some of the things were destructive.
When we were all gone, she went into her crate, and was no problem there, as there was no one home to pay attention to her.
When she was 2, we decided maybe another would help get her attention away from us.
It was the perfect solution, it took care of almost all her destructiveness. I guess she just needed someone, dog or human, to play with her. Sugar and Spicer!
I've said since then that she was the perfect 'first' basenji and taught us what we thought, not only how bad a baasenji could be, but also how endearing.
Then there was Ibis, who made Sugar look boring. She had separation anxiety, plenty of dogs to keep her busy, and all methods of dealing with her SA did not work. Oh well, she is the one basenji my husband and I cried as she was put down, at 16. After her, my life is so much easier.
Another dog would likely help with the separation anxiety but could also introduce other issues. Assuming you're not keen on a second dog, have you tried dog day care? Even once a week might help. Sometimes they just need to understand they can deal with things on their own.
@beth Try behavior training before you add another dog. This is going to take a bit of repitition over the better half of a morning, and a few days of follow up training -- but it works.
Do whatever preperation you normally do to leave. Tell your dog that you will be "right back" (insert whatever command word/phrase you want to use). Then exit and lock your door. Walk around the corner of the building, then return. Praise your dog as you greet them. Wash, rinse, repeat, gradually increasing the amount of time you are gone. Start at a few moments, then trips to the store, etc.
This reassures them that you will come back,. but you are actually teaching your pup the routine ques. It alerts the dog that you are preparing to leave (without them). Slightly different for when they get to go with you. Your dog will learn the difference ("Hey, if she picks up the leash, I get to go, too!").
I (personally) use bribes as a tell-tale. I give my pup a kong filled treat, or a frozen neck bone (her favorite) to chew on if she's staying at home. If I call her and pick up the leash, she's coming with. But she's ok, even on the rare occasion that I'm gone for 6 hours!