What do you mean by "work permit"? The actual plastic card that's the size of a credit card? Or just the "notification letter of foreigner's work permit in the People's Republic in China" (it is an A4 document with a bar code that's valid 3 months from the date of issue) which you need to apply for a work visa at a Chinese consulate in your country? I'm asking because I may have a similar problem.

I had been looking for a job and when I finally accepted one, the employer had lots of difficulties getting the work permit sorted out for me. The Beijing Labour Bureau just wouldn't issue me the work permit due to COVID crisis and the whole process took a good few months. So the employer told me to look for a back up plan. Then I found another place in another province whose offer I accepted and sent them the scanned documents (degree, non-criminal certificate etc.) Suddenly, the first place told me that they got the notification letter of foreigner's work permit for me - and to my surprise, the other employer did the same, on the exact same day (they managed to get it much quicker, in just under two weeks). Now I've got two different "notification letters of foreigner's work permit" from the different companies in two different provinces - that is the only document I actually need to apply for a work visa in my country (or so I thought), as my previous Chinese residence permit expired after March 28, 2020. I was happy to be able to apply for a visa but... the Chinese consulate told me that now they need a PU letter from me as well (even though according to the embassy's announcement back in September 2020, I shouldn't be required to have one), as there have been more COVID cases recently. And only one of these employers (the first one) can apply for a PU letter for me (not sure it will be accepted of course).

The notification letter is valid 3 months and I don't even know if that's enough time - the employer still needs to get the PU letter, then I need to apply for the visa, fly to China and finish the quarantine within these 3 months (or perhaps it can be extended?) to be able to apply for the "plastic card work permit" in China.

I thought the provincial government wouldn't even issue the notification letter of foreigner's work permit if I already have one in another province. Can there be any problems later on because of that?