Multiple entry or transit

We are Norwegians going to China and other Asian countries this summer. We will go through Beijing a total of four times. Can Norwegians get multiple entires? I see on the Chinese Embassy home page that we can not. We need to get out of the airport twice, one time because we are in Beijing two days. But the other two times we are in Beijing less than 24 hours. can we get two or multible entry transit G? Thanks