How many times can you use the Visa Free Transit?

US Citizen here and want to visit both Beijing and Shanghai using 2 separate visa free transit back to back.

Can I do let's say
Tokyo > Beijing (2-3 days) > Hong Kong
then right after
Hong Kong > Shanghai (2-3 days) > Tokyo

Is there a restriction to how many times I can avail the transit visa within a certain amount of time.

Thank you.