Internship in Shanghai

Hi! I am going to tongji University in Shanghai from sept to Decemeber as a semester abroad for my MBA. I currently work for a multinational firm that have an office there. I am not clear or whether or not I could do an internship with them while I am in China. Also is it possible to have two kind of visas at the same time? Meaning the student one that Tongji will give me and then get a work permit / Z for the 4 months I am there? Thanks