The Pierre Auger Observatory was built in Argentina to study cosmic rays with energy larger than 0.1 EeV. It applies two independent and complementary techniques to detect extensive air showers: an array of water-Cherenkov detectors (WCDs) and a set of fluorescence telescopes. About 40% of the events detected with the water-Cherenkov detectors, for energies larger than 30 EeV, present saturation. The installation of an additional photomultiplier tube (PMT) with small cathode area in the WCDs was proposed to overcome saturation. We analysed data from ten experimental WCDs equipped with small PMTs. We showed that the small PMTs can be calibrated using the standard PMTs. The mean calibration uncertainty was less than 1%, although some events presented uncertainty larger than 20%. A correlation of the calibration with long-term variations of temperature was found. Finally, we showed that the implementation of the small PMTs extended the dynamic range of the WCDs by a factor of 25 times, which reduced the overall saturation occurrence from 6% to less than 0.1%.