Why not send up a “re-transmitter,” or some sort of satellite to relay a strong signal from Galileo?
The project briefly studied this option, but quickly determined that, given the short amount of time in which the relay satellite would need to be designed and launched, a relay would be prohibitively expensive. There were also significant unresolved technical problems related to both orbital mechanics and telemetry. Engineers first proposed having a relay satellite that would follow Galileo closely, like a well-trained dog. But, the amount of propellant needed made the mission too expensive. Even keeping the relay satellite within a few million kilometers of the spacecraft throughout the entire two-year orbital tour would be a difficult (if not impossible) engineering problem, given the limited amount of propellant on board a relay satellite. Finally, the relay antenna itself would need to be comparable in size to Galileo’s original High Gain Antenna, which would add to the expense and complexity of a relay mission.
