Digital Tomosynthesis (DT) is a low-dose X-ray limited-angle tomographic imaging technique. It is a non-invasive and non-destructive method for three-dimensional imaging of the inner structures of an object. Nowadays, it is an attractive low-dose alternative to Computed Tomography (CT) in certain imaging applications. However, the data incompleteness is the major problem of DT. It results in the violation of tomographic sufficiency conditions, which, in turn, results in the limited axial resolution of the reconstructed images. Another problem is that for long objects the in-plane image quality depends on the in-plane orientation of the object with respect to the X-ray tube rotation axis. In the current study, tomosynthesis is considered for musculoskeletal imaging. Two challenging problems of limited axial resolution and image quality are addressed in the current work. A novel tomosynthesis acquisition scheme, based on a tiltable object-supporting platform, is proposed. The platform tilts the object in the direction perpendicular to the X-ray tube movement direction. It allows for acquiring additional projections by collecting information about an object from the sides, which improves the Radon space filling and better fulfils the Tuy-Smith data sufficiency conditions. The potential of the proposed acquisition scheme is validated both qualitatively and quantitatively using a software simulation framework. The simulations show two promising results. First, the axial resolution can be considerably increased compared to standard tomosynthesis acquisition geometry, while keeping the number of projections (i.e. dose) fixed. Second, the dependency of image quality on the object orientation can be decreased. Abovementioned results are reached without increasing the patient dose. Potentially, the hardware implementation of the proposed platform is very attractive, because it will not require any modifications of existing tomosynthesis devices.