Re-entry permit

Hi.
I'm going to visit China as Tourist (L) but I need a 3-entry, but there's no 3 or multi-entry one for tourists...
I will go to Guangzhou on June 26th and will leave to Cambodia on June 27th.
I will go to Shanghai and Beijing on July 11th and leave to Taiwan on July 14th.
I will go to Diqing on July 24th and leave from Shanghai to Mexico on August 1st.
What can I do? as longer as there's only single and double entry and the proccessing time at the PSB is 5 days.
Thanks in advance!