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 Gacs-Korner 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.
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