To answer your question, lots of people have -- which is why there are so many programs offered now. Some are good, some not so much. Some intense, some immersion 'lite'. It depends on the age of the child or if it is for yourself? Most
International Schools in Singapore have exchange programs, you could start there.
Also, if you google the Petersons guide, you could set the search options for studying in China (or anywhere) based on program length or age of child and academic focus. If you google 'student exchange programs china' you'll get a lot of options too. I know a few kids that found what they wanted through
www.chinesestudyabroad.org. As far as universities go, the same rules apply as finding any school with a good fit -- search for study abroad programs, look at each schools website and ask for information. Ask lots of questions. Good luck.