I've played the game a couple of times and both times the runner played the same piece of ice twice. If this happens do these two cards support each other (does the second one make the first stronger)?

I'm thinking it doesn't work like this, but I've read the rules and quite a few posts here, but I didn't see this situation before, so thanks for any advice.

In general, there's little point to playing the same icebreaker more than once (the big exception right now is Atman, but don't worry about that for now). Strengths do not get combined, or totalled, or anything else.

That's what I thought, thanks for confirming!