User Stories - How should it be defined for complex changes involving multiple applications

Question

This is one of the definitions that I asw for user stories -

When the time has come for creating user stories, one of the developers (or the product owner in Scrum) gets together with a customer representative. The customer is responsible for formulating the user stories. The developer may use a series of questions to get the customer going, such as asking if some particular functionality is desired, but must be careful not to dominate the idea creation process.

In a large organization there could be multiple lines of business. For a particular line of business , there could be multiple applications (more than 10) that may be involved in fulfilling a business requirement. The requirement to each of these application teams could be provided by a business analyst and the high level solution could be formulated by a solution designer.

In scenarios such as these , would a single user story be defined for a specific change request that impacts multiple applications or would different user stories be created for each application? If it is a single user story then would a separate SRS be defined for each impacted application would it need to be associated with the user story defined?