alt Hacker News...well actually...
There are more combinations than merely having only X, or an XY combination. And there is more fuzziness even in the Y and X expression, as you said. It's fuzzy all the way down. The tale of Binary results has always been from compression of reality: Always has been.
As it happens, in humans there is a single gene on the Y chromosome, named SRY, that typically switches on male-linked traits.
But you're right, the full range of biological possibilities is very fuzzy . SRY itself a just a regulatory switch that other sex-linked traits are conditionally dependent on. If the switch gets broken, you develop as female. If genes that support the switch break, you might develop as female. If a sex-linked trait downstream from SRY mutates, then pretty much anything can happen. And other species do sex determination completely differently. Hell, a lot of bacterial sex basically involves throwing pseudo-viruses at each other.