Can I normalize my data in order to compare it? I have three chromatograms of the same eluted protein but at different concentrations, since it got diluted during purification process) and hence peak maximums at very different absorbances.

The highest is around 100 AU and lowest 20 AU.
I want to present these and look at the difference in peak shape (because I want to look at aggregation). Can I simply multiply the data that generated the peak max at 20 AU by 5? Because then it is easier to compare the shapes of the peaks when they  overlay each other.

Is this something one would do or is it totally forbidden?

Thanks in advice.
I assume you have a UV/Vis absorbance based measurement. Then the absorbance should follow Beer´s Law which states that absorbance is proportional to concentration. Therefore you should be fine with your normalization approach. You could check if you are in the linear range by performing a calibration.