The Metis coronagraph of the Solar Orbiter (SolO) mission records full-Sun images of the solar corona in Lyman-α ultraviolet (UV) radiation and in visible light polarized brightness (pB). This work investigates the utility of a synoptic observational program of Metis in terms of using its pB-images for tomographic reconstruction of the three-dimensional (3D) distribution of the electron density of the global solar corona. During its lifetime, SolO’s distance to the Sun will range D ≈ 0.3−1.0 au, while its solar latitude will span θ ≈ ±33 •. The limitations that such orbit complexity poses on tomographic reconstructions is explored in this work. Using SolO’s predictive orbital information and 3D MHD simulations of the solar corona, time series of synthetic Metis pB-images were computed and used as data to attempt tomographic reconstruction of the model. These numerical experiments were implemented for two Carrington rotations, corresponding to a solar minimum and a solar maximum, representative of extreme conditions of coronal complexity. For each rotation images were synthesized from three orbital segments, corresponding to extreme geometrical conditions of observation by Metis. For the early phase of the mission (year 2023), simulations were carried from the largest aphelion (D ≈ 0.95 au) and the smallest perihelion (D ≈ 0.29 au), both cases corresponding to low latitude (|θ| < 10 •) positions. For the late phase of the mission (year 2029), a simulation was carried out from the maximum solar latitude position (θ ≈ +33 •), at an intermediate distance (D ≈ 0.5 au). The range of heights that can be reconstructed and the required data-gathering time, both dependent on D, are reported for the six experiments. The extension of the coronal region that can be reconstructed and the accuracy of the reconstruction, both decreasing with increasing solar latitude |θ| as well as with increasing coronal complexity, are discussed in detail in each case. As a general conclusion, a Metis synoptic observational program with a cadence of at least 4 images/day provides enough data to attempt tomographic reconstructions of the coronal electron density during the whole lifetime of the mission, a requirement well within the 2 − 3 hr cadence of the current synoptic program. This program will allow implementation of tomography experimenting with different values for the cadence of the time-series of images used to feed reconstructions. Its cadence will also provide continuous opportunity to select images avoiding highly dynamic events, which compromise the accuracy of tomographic reconstructions.