Broodiness is hormonal, you can't induce it.
Once the hen is a confirmed setter, she doesn't know what kind of eggs are under her. Some will set on golfballs. You can remove whatever she is setting on and put eggs of your choice under her. To be certain, do it after dark when she is asleep. Please mark them in case someone else wanders into the nest to lay while she is out pooping.
It's not advisable to let a hen set more than 4 weeks at a time. It takes a lot out of them and they lose weight. I've had luck grafting newly hatched chicks onto a setting hen or putting eggs with only a few days to go under a setter. They raise the chicks and return to lay in much better health than after a 3 week hatch.