AC amplifier with fixed output range?
An automatic gain control (AGC) appears to be what you want. It will try and keep the output constant by using a variable gain cell (usually a JFET) driven by a voltage that represents the peak magnitude of the output. If the output voltage signal level is too small the gain cell is rapidly compensated to achieve the correct amplitude.

You might also consider using a high frequency boost filter just to raise the amplitude of the input signal so that things are levelled out.