"Does that make you four uncles?" I said.
"No, that makes me a quadruncle," said Dan.
From which I concluded I must be a quadraunt.
I like the idea of coining new kinship terms, but really, this one doesn't clarify much that our culture needs, and it would make it harder to get by in high school French classes. Just imagine singing "Le Monocle de Mon Oncle" if you had to wonder whether you were hearing a person talk about a monuncle. Diuncle would probably get contracted to duncle, and diaunts might well become daunts--goodness knows, some aunts are plenty daunting. Worst, though, a person with nieces and nephews adding up to nine would be a nonuncle--too easily confused, if only in the pronunciation, with a non-uncle.
On the other hand, some of us would get to have, or be, dodecauncles, and that's hard to resist.