As rabidcow points out, non-count nouns cannot be made plural as they are in a sense already plural. For instance mud, as in "some mud, even more mud", similarly sand, faeces, dirt, water, rice, snot, porn, love or weather.
Yes, in the English language, baggage is a diffuse heap of stuff, not a discreet item. Don't blame me, I didn't do it.
words that are their own plurals are not non-count nouns. You can correctly say "one elk, many elk" or "one fish, many fish". The word's ending may not have changed, but the concept can be expressed in singular or plural. On the other hand, "One advice, many advice" is not correct English at all. "some advice, even more advice" or the singular form "a piece of advice" are correct.
Re the idea that "data" is plural, the word data was originally the plural of datum, but is often used these days as a non-count noun. We've got so much of it these days.
Plurals are sometimes used to refer to different kinds of the substance. e.g.: Where the fresh water from the river meets the salt water of the sea, there is a confluence of the waters.