  We study a variant of the successive refinement problem with receiver side
information where the receivers require identical reconstructions. We present
general inner and outer bounds for the rate region for this variant and present
a single-letter characterization of the admissible rate region for several
classes of the joint distribution of the source and the side information. The
characterization indicates that the side information can be fully used to
reduce the communication rates via binning; however, the reconstruction
functions can depend only on the G\'acs-K\"orner common randomness shared by
the two receivers. Unlike existing (inner and outer) bounds to the rate region
of the general successive refinement problem, the characterization of the
admissible rate region derived for several settings of the variant studied
requires only one auxiliary random variable. Using the derived
characterization, we establish that the admissible rate region is not
continuous in the underlying source source distribution even though the problem
formulation does not involve zero-error or functional reconstruction
constraints.
