I haven't done this myself but given that ELF does not have a dedicated .stack region, I guess you first have to find out what memory address range will ELF use to store variables on the stack.

Finding out the beginning of the stack should be possible to deduce from memory addresses upon entering the main().

Finding out the end of the stack depends on how big the stack is and whether it grows upwards or downwards. Former is of dynamic nature but usually configured at system level on Linux and for the latter I am not sure but I think it grows downwards.

IMO the easiest way (but certainly not the only way) is to allocate a new stack and switch to it with makecontext(). The manpage has a full code example. You just need to change the stack alloc. This approach has a few drawbacks but is hard to beat in terms of simplicity.