We need more details? What do you mean by to make a button? What kind of profile question do you want it to be?

I mean to make button - "add". E.g. In admin I add new question - school. And it has panel - "Do you want to have button - add". And near type multiple choice with one value - Yes.

In My Profile->edit profile details it looks like photo.png

I hope that I clearly explained.

This is a custom code modification

This can't be done by default from the admin panel. This requires code modification

we'll think about it.