I have a function that is called for several distinct reasons.  It is
conceivable that a subclass would want to handle those cases differently.
Therefore, what I want to do is have multiple v-table slots, all pointing to
a common base function.  These functions should be protected, not public.

Here is a short example of what I'm trying to accomplish:

class XYZ
{
protected:
virtual bool SupportsX();
virtual bool SupportsY();
virtual bool SupportsZ();

virtual bool NoSupport() = SupportsX, SupportsY, SupportsZ;
};

bool XYZ::NoSupport( void ) { return false; }

Except that in my case the common default function is considerably more
complicated, and I don't want to repeat the code everywhere.

The compiler gives me:
error C3653: 'SupportsX' : cannot be used as a named override: a function
being overridden not found; did you forget to name the function explicitly,
using a :: operator?

Right now I've worked around this by adding an extra inheritance level -- an
abstract base class that defines pure virtual functions that I can
explicitly override, but that really shouldn't be necessary, because there's
no technical reason the compiler can't introduce a new set of v-table slots
and fill them all with the same method pointer.  Am I just missing the right
syntax?