The ALPACA experiment aims to observe sub-PeV gamma rays in the southern hemisphere with a new air-shower-array observatory. The observatory is located at an altitude of 4,740 m above sea level on Mt. Chacaltaya, Bolivia. A new surface air shower array plans to consist of 401 scintillation detectors covering an 83,000 m^2 surface area. Each scintillation detector is equipped with a 2-inch-diameter photomultiplier tube (2-inch PMT). The 2-inch PMTs detect the scintillation light produced by shower particles passing through the plastic scintillators and reconstruct the energies and directions of gamma rays and cosmic rays. In this paper, the extension of the maximum measurable number of particles within the linearity range of the PMT, the so-called dynamic range, is studied by reading out (electronic) signals from one of the dynodes of the PMT. As a means of extension, in addition to the normal anode signal, the signal is read out from the dynode, which is in the middle of signal amplification. Our results show that the 2-inch PMT, R7724, produced by Hamamatsu Photonics has achieved a dynamic range of about 500 particles with dynode readout from the seventh of a total of ten dynodes. This enables the accurate determination of the energies of gamma rays up to about 2PeV.