In the multiple descriptions (MD) problem with L channels, a decoder is said to be in Level α (1 ≤ α ≤ L) if it can access a subset of α encoders. We extend the MD problem by imposing an additional distortion criterion, called the subset distortion criterion, for each subset of reconstructions. The subset distortion criterion can be interpreted as in some sense forcing consistency within a subset of reconstructions. A special case of the subset distortion criterion, called the pan-level distortion criterion, is when the subset consists of reconstructions in the same level. With this formulation, we can include both the MD problem and the symmetrical multilevel diversity coding (SMDC) problem as special cases. Under this light, we prove an inner bound for the extended MD problem which is tight for a special case in which the reconstructions within the same level are required to be essentially identical.