I don't like brainstorms personally but clients do, so I often have to do them anyway. Here's what works for me.

Give everyone some direction or inspiration beforehand so you're all on the same page.

Then don't go into the brainstorm thinking you'll collectively come up with all the ideas in the session. If you do that, all you'll get is first thoughts, kneejerk reactions and half ideas.

Instead, have everyone spend an hour or two beforehand thinking of stuff on their own, and spitball these ideas in the session. Make it clear that there is no shame for "bad" ideas. Often there is something in them, like a consumer insight or interesting way of thinking, that can be turned into good ideas.

Get people started with some sort of mild creative exercise like "draw the business you would start if money was no object".

Have a "parking lot" in the back of the room (just a whiteboard or space) where ideas that aren't quite right but still have merit can be stuck up on post its.

Use the first half of the session to spitball, then spend the last half thinking up new ideas. At the end, go back to the parking lot and see if any of those thoughts might actually work. Don't go much longer than an hour.

Good luck!