This does not appear to be about the iostream limitation but about design. That is, your assignment is to craft/create this mini-app. So I can't write code for you but share that you need to step back and design before code.
That is, you know you need an outer loop to keep going till exit. Then an inner loop to hold that menu and perform those actions. I don't see you using any loop construct. Look up do and while on the usual tutorials.