My dr just gave me a birth plan to fill out and take to the hospital with me and that is included in it (there's a bunch of questions and options). It asks how you want to be involved in her delivery or something, asks if you want to touch her head, have a mirror available to see, if you want the baby put on you immediately after, and help pulling the baby out(catching the baby) is one of the options. So I'm sure you could but idk how much they would follow the birth plan. Just be sure to mention it to the dr and nurses who are going to deliver your baby while you're in labor!