There is an expression used when you invite, or give advice to, someone, "how about -ing?". Regarding this, my question is whether or not it's possible to add a genitive personal pronoun, just like the following expression:
Do you mind my/your opening the window?
For example, is the following example correct?
How about your going to see her in the hospital? (To recommend the hearer, not anyone else, seeing a woman in the hospital)