The coded aperture snapshot spectral imaging (CASSI) architecture has been employed widely for capturing hyperspectral video. Despite allowing concurrent capture of hyperspectral video, spatial modulation in CASSI sacrifices image resolution significantly while reconstructing spectral projection via sparse sampling. Several multiview alternatives have been proposed to handle this low spatial resolution problem and improve measurement accuracy, for instance, by adding a translation stage for the coded aperture or changing the static coded aperture with a digital micromirror device for dynamic modulation. State-of-the-art solutions enhance spatial resolution significantly but are incapable of capturing video using CASSI. In this paper, we present a novel compressive coded aperture imaging design that increases spatial resolution while capturing 4D hyperspectral video of dynamic scenes. We revise the traditional CASSI design to allow for multiple sampling of the randomness of spatial modulation in a single frame. We demonstrate that our compressive video spectroscopy approach yields enhanced spatial resolution and consistent measurements, compared with the traditional CASSI design.