Apparently Birmans aren't fussed about whether their companion is another Birman, a different type of pedigree cat or just a moggy. My parents used to have one and it got on fine with all the other pets that were introduced to it. So I guess it's up to you what you get really and what will suit you best!
If you feel like another Birman then go for it or maybe try another breed but perhaps something with a similar temperament. I don't know a lot about many breeds, in the past I've had a Burmese. It was an experience I have to say - they're noisy and quite highly strung. My new love is the British Blue - such lovely, sweet cats with a fantastic nature. Maybe it'd help to do some research on breeds and choose one to suit?
Or the alternative is to visit a local shelter, they always have kittens/cats and you'd be giving one a great home. It wouldn't necessarily want to go outside, many people have non pedigrees that are indoor cats and if you live by a main road it's the safest option by far.
Anyway good luck finding a new addition!