Absolutely possible! Shooting stars are simply small bits of space debris (rocks, old satellites, waste from the International Space Station) that heat up when they hit the top of the Earths atmosphere. As they heat up, they leave a streak of light across the sky, since they’re moving so fast.
If 2 collided, there would be a tiny little explosion (nothing strong enough to do any damage to us) but it would be quite bright! So keep your eyes to the skies on dark nights, you’d never know if you’ll see a collision 🙂