Stops along the Bullet Train route from Shanghai to Beijing

We want to travel from Shanghai to Beijing and make a couple of stops along the way at cities that may be interesting to visit for a day or so. Does anyone know if we can do that - to stop our journey and continue the next day if we start from Shanghai to Beijing? Or do we just pay for the sectors we want instead of the Shanghai to Beijing fare? We plan to travel on the fastest Bullet one - I have to check what alphabet they give this service. Many thanks if anyone can help.