Funny you mentioned tuvan throat singing. I've actually been working on that lately. I start to have it under control too.
Anyway, What I try to do is to learn to use overtones in a controlled way in normal western singing. You can create clearly audible overtones in normal singing just by controlling how much you open the mouth, your tongue position, choice of vowel etc. I'm not trying to "sing harmony with myself" but to create a more powerful sound. I think that is fully possible.
Regarding plain singing, I'm working on the U2 song "Bad". Most of it goes well, but the highest part is giving me trouble ("I'm wide awake..."). I can sing the phrase in curbing well (it goes up to C# above the "tenor high C"), but I'm trying to find the Belting mode to make it more powerful (see
this page for definitions of curbing and belting. Curbing is almost synonym to "mixed-voice" and belting is a "screaming" mode). I just have trouble finding this Belting mode this high up in the register. I know it is possible to do it and I know what I should do but it is still freakin' hard... Well, not even Bono sings this in the original key live, and on the record you hear him struggling with this phrase a couple of times. Live I think he cheats on this phrase...
Here's the song (studio version):
http://www.youtube.com/watch?v=V2kDzJ5hsbw
The difficult part is exactly three minutes into the song, and in the end as well. I can do this song a half a step down but not in A. I don't like to transpose or tune down so I want to nail it in A too. Guess I need to work harder...
