Using a question mark mid-sentence [multiple question marks] when a question is ...

May I use a question mark in the middle of a sentence?

Examples:

Would you like the drapes to be white? or perhaps something off-white?

Would you like the logo to be centered? at the bottom? left off entirely?

I've mainly seen these in older literature, usually used in dialogue, but sometimes in rhetorical essays. It is rare in common and modern writing. I'd advise against it.

You should either capitalize or rephrase/repunctuate:

Would you like the drapes to be white? Or perhaps something off-white?

Would you like the logo to be centered? At the bottom? Left off entirely?

Or:

Would you like the drapes to be white; or perhaps something off-white?

Would you like the logo to be centered or at the bottom? Should it be left off entirely?

The former change (capitalizing) is more informal than the latter suggestion; also, the latter can be legitimately tweaked in several places based on context.