actually this happened to me when i first came here three years ago.  i accepted an offer from one school, and also interviewed with another school the same day.  the latter assumed (i have no idea why) that since i interviewed with them i had accepted their offer.  so within a week's time, i received two invitation letters for working visas.  i decided to take both of them to the Chinese embassy/consulate in San Francisco and be honest with them and tell them what had happened.  i believed, and still believe, that when ever you are dealing with your visa and other legal documents in china, honesty is the best route to choose.  the lady at the embassy just laughed and said i must have good people skills for two schools to fight for me and asked me which school i preferred.  i paid the express fee and got the Z visa in a few hours. 

now that i look back on it though, i should have chose the other school.  i ended up having a huge argument with the first school's principle and terminated my second contract with him early... but that my friend, is a story for another day..

In the case mentioned the State Admin or Foreign Expert's Affairs won't issue two Work Permits, or invitation letters.

But apparently it is possible to have two employers listed on one Work Permit - if you can get permission from both.