Do you think that Voldemort can actually be classed as Mind, Body or Spirit? You've said that you can see all three parts inside him, but he, to me, is very tricky to pin down. Perhaps it is simply that we do not know enough about him, although the trips into his childhood in HBP confuse me. I might have classed him as a body character (driven by greed and self-protection), or a spirit (his independence) but there are elements of mind in there as well. I honestly don't think he can be classed as either Mind, Body or Spirit. What you said about him being the shadow to Dumbledore was very interesting, but I'm not even sure, like you said, that he can be put into that category. I think he'd be quite happy not being the antagonist to anyone, simply standing alone.
Honestly, I think Voldemort stands alone. For one, I don't think we know enough about the "bad guys" to really try to pair them off, or establish trios like we have among Harry's friends or the Maruaders. Second, I think one can see the three parts - mind, body, spirit - within Voldemort quite a bit more clearly than in others. I think because of that, he works alone: he was born alone, he grew up alone, he went off alone, he fights death alone, he rules alone.