Madrid-shanghai-tokyo tokyo-shanghai- madrid

Hello, we have bought two full trip tickets, one Madrid Shanghai and other Shanghai Tokio.

On our first stop in Shanghai we won't leave the airport. However as we are not flying with the same air company we Will need to get the suitcases and maybe get through the border.

In our second stop in Shanghai we want to visit the city during three days. Can we get here a transit entry permit?

Is it possible to get two transit visa within three weeks if needed?
Thanks!