Handling unexpected features during sprint

Question

Our team is going to adopt scrum and agile technics. We've got a product, which we develop for multiple customers. This customers supplied us with necessary requirements, so everithing is fine to adopt agile techinics.

But at some moment (for example during sprint), new customer apears, and he wants to get a demo of product slightly different from what we have now. This may be some new features or minor differences in behavior. And he wants to get this demo for example during the week. It is very important to show that our product supports this features (because otherwise he will address to our competitors), so we have to develop this features (may be partly) during the week.

How we must handle this sort of features with agile? Move them to current sprint backlog? Or split one team to two and create another sprint? Or may be there is another way?