Can you give the circuit diagram ....
I think with higher gain the swing of the output signal is increasing. Can your output stage tolerate that swing. If no then the peaks of the signal might get saturated (chopped off). Increasing distortion and introducing higher harmonics.
I do not know what you are using for your PGA.
If it is an opamp then it has negative feedback. The negative feedback reduces its output distortion and makes its voltage gain less.
When its voltage gain is higher then its distortion is also higher.