It may be ideal to have your Scrum team focus on a single story first, complete it with compliance of their definition of done, and then move on to the next story, but in practice we are yet to achieve it. What we have found works best for us is we work like small surgical teams where one developer is assigned the chief responsibility of a surgeon for a story and another (or more) developer is tagged along with him as copilot/assistant. That copilot knows all the details about the work on progress and can act as an alter ego of the chief surgeon when she/he is not available. The situation may be reversed in some other story/module of the product where the previous copilot is playing the role of chief developer, and the previous chief is playing the role of a copilot.
Scrum synergies the chiefs of each story and also the copilots so that everyone is on the same page regarding the goal of a sprint, and overall product goal. When a conflict arises between two chief surgeons where one is needed as copilot for the other one, we fall back to the prioritized sprint backlog and complete the higher priority story first, then concentrate on the later ones even if it means leaving some stories undone.