We explore the problem of view synthesis from a narrow baseline pair of images, and focus on generating high-quality view extrapolations with plausible disocclusions. Our method builds upon prior work in predicting a multiplane image (MPI), which represents scene content as a set of RGBA planes within a reference view frustum and renders novel views by projecting this content into the target viewpoints. We present a theoretical analysis showing how the range of views that can be rendered from an MPI increases linearly with the MPI disparity sampling frequency, as well as a novel MPI prediction procedure that theoretically enables view extrapolations of up to 4 times the lateral viewpoint movement allowed by prior work. Our method ameliorates two specific issues that limit the range of views renderable by prior methods: 1) We expand the range of novel views that can be rendered without depth discretization artifacts by using a 3D convolutional network architecture along with a randomized-resolution training procedure to allow our model to predict MPIs with increased disparity sampling frequency. 2) We reduce the repeated texture artifacts seen in disocclusions by enforcing a constraint that the appearance of hidden content at any depth must be drawn from visible content at or behind that depth.