The G4S_2.0 project - financed by the Italian Space Agency (ASI) - aims to perform a set of measurements in the field of gravitation with the two Galileo satellites GSAT0201 (Doresa) and GSAT0202 (Milena) exploiting the relatively high eccentricity (≅0.16) of their orbits with respect to that (≅ 0) of the other satellites of the Full Operational Capability (FOC) constellation and taking advantage of the accuracy of their on-board atomic clocks: two Passive Hydrogen Maser (PHM) clocks and two Rubidium Atomic Frequency Standard (RAFS) clocks. On the contrary, the entire Galileo FOC constellation is considered to place constraints on the presence of dark matter in the Milky Way.