Here's an opener I was inspired to start trying, after I've already built some rapport with a woman.
Me: Hi, I need your opinion on something.
Me: My friend Chelsea (or any girl's name, important that it's a girl, as it shows there is competition) and I were having a debate about whether guys and girls can be just friends. I think they can be, but she says that guys always want more. What do you think?
That last line is important, because in reality, guys normally say that guys and girls can't be just friends, and girls say that they can. By reversing it, you've false disqualified yourself (albeit weakly, but you've shown her potential that you could put her in the "just friends" category), and you've also given her the notion that there is another girl you've been talking to (who doesn't think you can be just friends with a girl).
I think it is a good opener, but I don't know how to further the routine past that, based on what her answer is. Any feedback?