  The sum formula for finite and symmetric multiple zeta values, established by
Wakabayashi and the authors, implies that if the weight and depth are fixed and
the specified component is required to be more than one, then the values sum up
to a rational multiple of the analogue of the Riemann zeta value. We prove that
the result remains true if we further demand that the component should be more
than two or that another component should also be more than one.
