This kind of device is called a "compressor", and they are ubiquitous in recording studios. They can get very expensive and complicated, but for your purpose something like this may suffice:
Specifically what you want is a "stereo compressor" or "compressor/limiter"; if you want something more sophisticated than the device above, there are many 1U rack options available for ~$200 (dbx is a good choice), or used on reverb.com more like $70-$100.
https://www.amazon.com/rolls-SL33B-Stereo-Program-Limiter/dp...
Specifically what you want is a "stereo compressor" or "compressor/limiter"; if you want something more sophisticated than the device above, there are many 1U rack options available for ~$200 (dbx is a good choice), or used on reverb.com more like $70-$100.