You can run multiple instances of Claude Code at the same time.

I know, I do it all the time! I wasn't calling out 240 hours as being impossible to hit in 168 hour weeks. I suppose "does not really look limited" could be read multiple ways - I did not mean it's literally unlimited, just that it doesn't look very limited.

You can make your own comparison to however many hours you usually spend working in a week and how many sessions you have active on average during that time.