Interrupting someone gracefully is always challenging. People don’t like to be interrupted and they don’t like interrupters.
Here are a few ‘word tools’ that work every time.
1. ‘Excuse me for interrupting, but you sparked an idea…’
2. ‘Excuse me, did you say… (repeat back what they just said), that reminds me that I didn’t have the chance to share with you that… (or some variation)