Why can’t I increment a variable of an enumerated type?

I’m probably overlooking something obvious, but what’s a good substitute?

Overloading operator++:

// Beware, brain-compiled code ahead! 
StackID& operator++(StackID& stackID)
{
#if MY_ENUMS_ARE_CONTIGUOUS && I_DO_NOT_WORRY_ABOUT_OVERFLOW
  return stackID = static_cast<StackID>( ++static_cast<int>(stackID) );
#else
  switch(stackID) {
    case value1 : return stackID = value2;
    case value2 : return stackID = value3;
    ...
    case valueN : return stackID = value1;
  }
  assert(false);
  return stackID; // some compilers might warn otherwise
#endif
}

StackID operator++(StackID& stackID, int)
{
  StackID tmp(stackID);
  ++stackID;
  return tmp;
}