Slice-stacking displays are particular kind of volumetric displays, which present a large number of volumetric elements to viewers. These elements are typically packed in a 2D array, called “slice” or “depth plane”, which sequentially fills a 3D volume. Recently, multilayer displays have been proposed and implemented by several researchers. Unlike slice-stacking displays, multilayer displays can present multiple slices at the same time. Furthermore, slices in multilayer displays always remain stationary, i.e., there are no sliding or rotating slices, which are often found in slice-stacking displays. In this paper, we consider a mixture of slice-stacking and multilayer displays. More specifically, we present a new design of multilayer displays, where slices will move periodically and translationally changing the relative distances from the viewers. By allowing the slices to move around, we can, in effect, increase the number of layers in the displays. This results in finer resolution of the light field observable from the displays, and improvement in the precision of the accommodation cues. An implementation of the new design using a beam splitter and a single moving mirror is also presented along with a few experimental results.