Capitalization of plural noun given proper adjective and common adjective

I've recently come across a dilemma of whether to capitalize a plural noun, given that it's described by a proper adjective (like a place) and a common adjective (a descriptive adjective).

Example-

...big and Saharan deserts

Or

...big and Saharan Deserts

In both of these cases, we're talking about multiple deserts, and one is big, and the other Saharan. Does desert get capitalized? Would the order of the adjectives matter?

I know it's not a great example (I'm not talking specifically about the Saharan Desert, but any proper adjective would do), but can anyone clarify? I've never learned about this specific topic (with one proper and one descriptive adjective). Also, if a question like this exists, please kindly direct me to it! Thanks!