In this paper, we explore the spatiospectral image super-resolution (SSSR) task, i.e., joint spatial and spectral super-resolution, which aims to generate a high spatial resolution hyperspectral image (HR-HSI) from a low spatial resolution multispectral image (LR-MSI). To tackle such a severely ill-posed problem, one straightforward but inefficient way is to sequentially perform a single image super-resolution (SISR) network followed by a spectral super-resolution (SSR) network in a two-stage manner or reverse order.