Can I transit 2 times? That is: 1 transit outbound and 1 transit inbound

It is fine to have two separate stopovers NOT EXCEEDING 144 hrs EACH. Just apply in Beijing and Shanghai as usual respectively.
Make sure you hold one of the passports listed above and you have an onward ticket to OUTSIDE MAINLAND CHINA ❨not incl. HK/ Macau/ Taiwan❩. Pls take note that you are NOT ALLOWED to venture out of the Beijing region and Shanghai region during the respective stopover.
Hope this help.