240 visa-free transit - can I have layover in China on the outbound and return flights?

I am planning on entering China in Shanghai and activating the visa-free transit from then. However, I am looking at flights which will have a short layover in another Chinese airport (during which I don't plan to exit the airport). Will this be fine when I get to Shanghai? Also, the same issue will likely happen on the way back - i.e. when flying home from the 3rd destination, the flight will also have a short layover in China. Will this be allowed if I have already completed the 240 hour visa-free transit? Thank you!