I understand that an id must be unique within an HTML/XHTML page.
My question is, for a given element, can I assign multiple ids to it?
Nay.
https://www.w3.org/TR/2011/WD-html5-20110525/elements.html#the-id-attribute
The value must not contain any space characters.
id="a b" <-- find the space character in that VaLuE.
id="a b"
That said, you can style multiple IDs. But if you're following spec, the answer is no.