Theoretically, you can cascade 4 PGAs with a gain of 48 each. But the practical gain is limited by many factors:
a) Offset voltage: The maximum PGA offset is 10mV which is multiplied on 48. It provides 480mV of maximum offset. It can be removed by AC coupling between stages. If DC-component signals are required to be processed, this offset has to be taken care of by externally providing an offset compensation. In case, the output is processed by an ADC, offset compensation may also be provided in firmware.
b) Noise: PSoC amplifiers are not very quiet; the main component is 1/f noise, which is about 100nV/rt-Hz at 1khz.
c) Amplifiers interference: Such as all PSoC amplifiers are placed on same die including routing, the attempts getting high gain by amplifiers cascading can get parasitic oscillations.
Max gain of PGA is 48, with 3 dB point at 80 kHz. Cascading 3 PGAs result in gain of 110000. They must be AC coupled from one to the next, or offset voltage would make the gain useless. This could be very, very noisy, but possible.