Damavand intraplate stratovolcano constructed upon a moderately thick crust (58–67km) over the last 2Ma. The erupted products are dominantly trachyandesite-trachyte (TT) lavas and pyroclasts, with minor mafic magmas including tephrite-basanite-trachybasalt and alkali olivine basalts emplaced as cinder cones at the base of the stratovolcano. The TT products are characterized by a mineral assemblage of clinopyroxene (diopside-augite), orthopyroxene (clinoenstatite), feldspar (An2–58, Ab6–69, Or2–56), high Ti phlogopite, F-apatite, FeTi oxides, and minor amounts of olivine (Fo73–80), amphibole and zircon, whereas olivine (Fo78–88), high Mg# (80–89) diopside, feldspar, apatite and FeTi oxide occur in the mafic magmas. The presence of hydrous and anhydrous minerals, normal zonings, mafic cumulates, and the composition of magmatic inclusions in the TT products suggest evolutionary processes in polybaric conditions. In the same way, disequilibrium textures - including orthopyroxene mantled with clinopyroxene, reaction rim of phlogopite and amphibole, the coexistence of olivine and orthopyroxene, reverse, oscillatory and complex zonings of pyroxene and feldspar crystals - suggest magmatic evolutions in open systems with a varying temperature, oxygen fugacity, water as well as pressure and, to a lesser extent, melt chemistry. Mineral assemblages are used to model the physicochemical conditions and assess default parameters for the thermodynamic simulation of crystallization using MELTS software to track the P-T-H2O-ƒO2 evolution of the magma plumbing system. Thermobarometry and MELTS models estimated the initial nucleation depth at 16–17kb (56–60km) for olivine (Fo89) and high Al diopside crystals occurring in the mafic primary magma; it then stopped and underwent fractionation between 8 and 10kb (28–35km), corresponding with Moho depth, and continued to differentiate in the lower crust, in agreement with the geophysical models. The mafic rocks were formed by crystal fractionation from the reconstructed primary magma (13wt% MgO) with the minor role of recharge and crustal assimilation. Phenocrysts in TT lavas recorded a wide range of temperature and pressure of crystallization; at least three main levels of magma storage can be recognized according to the statistical analysis of the models, at 6–8kb (22–28km), 4–6kb (15–22km), and 0.6–3kb (2–11km), respectively. The temperature of crystallization ranged from 1430 to 1180°C for primary mafic magma to alkali olivine basalts and 1180–800°C for TT suite. According to the current geophysical models, the present structure of the magma storage system in the crust beneath the Damavand volcano consists of three major accumulation zones located at 20km, 6–8km and 3–4.5km depth. Our data enlarge this scenario, suggesting a more complex magma storage system strongly controlled by the transpressional tectonic regime. Multi-depth magma reservoirs may account for the local thickening of crust below the volcano. The polybaric fractionation model, using the MELTS algorithm, reproduces mineralogy and chemical variations of minerals and whole rock of the Damavand TT lavas. However, some discrepancies between major elements of models and trends of data can be ascribed to the recharge of more mafic magma, minor crustal assimilation, disaggregation of crystal-rich mushes and uptake of magmatic inclusions, as well as crystals from different crustal levels. The polybaric differentiation as the fractionation and/or accumulation of crystals was the probable mechanism for explaining the scarcity of mafic volcanic rocks at the Damavand volcano.