My input will be a bit non-direct and speculative as I have noticed the same issue on many movies and a few TV shows but I do not think it is actually a âPlexâ problem but rather more an encoding and even an original source problem.
Many shows are originally designed for movie theaters only and the acoustics there of and they are designed to be played at a VERY high volume. There is no intention of the audio being listened in the relatively small confines of the typical living room or even home theater.
Many, but not all and possibly not even most, receivers and other home audio decoders are designed with this in mind and they compensate for the apparent imbalance and make the music and other noises closer in volume so that the one does not overwhelm the other.
Unfortunately this is not usually adjustable and force those of us that prefer a more balanced experience to take other measures. I do not use any advanced audio, above Dolby 2.1, because of the excessive volume that much content has for things other than dialog. If I placed the volume, even on the best receiver I have tested, at a level where I can hear the dialog on much of the media I have then my neighbors two doors down or across the street would complain.
My solution is to only use Dolby stereo and pass that through a volume limiter. The one I use is this:https://www.amazon.com/Terk-VR1-Automatic-TV-Controller/dp/B00008VWOJ/ref=sr_1_3?ie=UTF8&qid=1467232021&sr=8-3&keywords=volume+limiter I have two and I hope they never fail because the price has nearly doubled since I acquired mine and their availability is becoming VERY limited. There have been devices like that designed for optical and HDMI but Amazon pulled all of them and I do not see them elsewhere either. I suspect that those did not and do not work at all well and so had too many complaints.
Some receivers and TVs have similar functionality built in but I have not seen any that work well.
I used to think that volume limiting functionality belonged outside Plex BUT I am now of the opinion that it is functionality that Plex actually needs and should have but it would need to be able to be completely disabled and disabled should be the default. But Plexâs desire for limiting user choices and user configuration makes anything like that quite unlikely.
I do not expect that content makers will ever go back to producing content with balanced audio so the âfixâ will have to be external for those of us that do not wish to listen at high volumes and/or do not wish to offend our neighbors particularly in apartments.
It is possible that the innovations in headphones might produce a truly comfortable, wearable and listenable experience but, so far, all headphones Iâve tried fall well short of comfortable usability for extended listening. But they have become a lot better recently and I hope they may get to the point where I find them usable.
The modern innovations in audio are not aimed at the user that wants a full experience without excessive overall volume and I do not see that changing so I very much doubt that there is a solution for you other that using the encoding process to âfixâ the audio as you have already discovered.
Sorry I could not provide a solution. 
