Multiple-image radiography (MIR) is an analyzer-based phase-contrast x-ray imaging method, which is emerging as a potential alternative to conventional radiography. MIR simultaneously generates three planar parametric images containing information about scattering, refraction and attenuation properties of the object. The MIR planar images are linear tomographic projections of the corresponding object properties, which allows reconstruction of volumetric images using computed tomography (CT) methods. However, when acquiring a full range of linear projections around the tissue of interest is not feasible or the scanning time is limited, limited-angle tomography techniques can be used to reconstruct these volumetric images near the central plane, which is the plane that contains the pivot point of the tomographic movement. In this work, we use computer simulations to explore the applicability of limited-angle tomography to MIR. We also investigate the accuracy of reconstructions as a function of number of tomographic angles for a fixed total radiation exposure. We use this function to find an optimal range of angles over which data should be acquired for limited-angle tomography MIR (LAT-MIR). Next, we apply the LAT-MIR technique to experimentally acquired MIR projections obtained in a cadaveric human thumb study. We compare the reconstructed slices near the central plane to the same slices reconstructed by CT-MIR using the full angular view around the object. Finally, we perform a task-based evaluation of LAT-MIR performance for different numbers of angular views, and use template matching to detect cartilage in the refraction image near the central plane. We use the signal-to-noise ratio of this test as the detectability metric to investigate an optimum range of tomographic angles for detecting soft tissues in LAT-MIR. Both results show that there is an optimum range of angular view for data acquisition where LAT-MIR yields the best performance, comparable to CT-MIR only if one considers volumetric images near the central plane and not the whole volume.