First of all, I'd say it is very rare to have someone getting stuck in a case and running completely out of options; the main cause for this kind of situation is probably a flawed / incomplete design of the framework.
To avoid this problem I think it's better to take enough time in the beginning of the interview to list all of the elements to be considered in the solution of the case, if you have practiced enough cases it is unlikely you are going to miss major points. In case that still happens most likely the interviewer will make you think about more elements to be added to the framework instead of working with you on a potential solution he already knows won't work. The importance of the framewrok is given by the fact that the most logical and effective solution whenever you get stuck, or more simply when you have to move to the next step in the case, is looking back at the initial structure and checking what's still missing.
Keeping composure is very important because the interviewer will want to test your ability to perform under pressure in front of a client so try to always show that you are proceding following logical steps and that the situation is under control (it's difficult, off course, but panicking won't help you at all), for that to happen don't be afraid to ask for some time to think about what you are gonna do next: the most common mistake you can make in those situations is trying to get unstuck by telling something you haven't really reflected on.