Dynamic compression in speakers themselves?


The primary audio characteristics I want to achieve in my system is an open, uncompressed, unstrained, and highly dynamic presentation.  What I don't know much about is how much speakers can or do contribute to loss of dynamics and impact.  I have a very powerful amp, but it seems that when I increase the volume, yes, the speakers get louder, but perhaps not commensurate with the increase in the volume control.  I do think I understand that this type of presentation is more easily achieved with larger scale speakers, but even with my large speakers, I feel something is wanting. 

I guess my question is, what factors contribute to any compression occurring in the speakers themselves?  Also, can the age of a speaker cause a loss of dynamics?  Mine are ~20 years old.  I'm thinking to get new speakers in the foreseeable future, so I'd like to understand more about this.  This question is in regard to traditional dynamic speakers.
mtrot
@mtrot 

Large pro studio (not PA) versions of ATC, PMC, Westlake, JBL, Genelec, Quested and Tannoy are all worth checking out if you seek big open dynamic sound and good vocal and timbre. Any of these makes with at least one 15” woofer would be a good start. 
Check out Von Schweikert Audio speakers, particularly VR 55 and above -  one of their primary goals is to create great dynamics . I play moine in large room for long periods at classical concert volume and can play for hours without fatigue

"Yes, I want the big, open, dynamic sound, but I also want great vocal tonality and timbre of instruments."

So does everybody and their brother on this site. Set a budget, pick a few brands/models within that budget, and ask for input specific to those models. Unless this is just a technical discussion about how loudspeaker drivers operate under stress.

"Unless this is just a technical discussion about how loudspeaker drivers operate under stress."

Well, yes, that is mostly what this thread is about.  And not just with regard to the drivers themselves, but how they work in concert with the other components and from whence any dynamic compression might arise.  And to what degree the age of components within a speaker contributes to compression.  As I posted above, "I feel that understanding more about this issue will be of use to me when considering future speaker purchases."  Also, you might refer to my original post.  Thanks to all for sharing their technical knowledge and expertise.
@mtrot - Magico has all their crossovers made by Mundorf. Quality commensurate with speakers grade.

Focal - Seems to OEM Solen/SCR mid-grade stuff for the most part. Horrible sounding caps IMHO.

B&W - Also a Mundorf user (but AFAIK build their own crossovers). They sometimes use the crossover grades to distinguish between speaker grades.

Monitor Audio - Uses OEM film caps, not sure who actually is the source.

Lawrence - Mid-grade Mundorf. Good sounding stuff appropriate for speaker prices.

Selah Audio - Uses top grade Clarity (my faves) among some models.

DeVore - Clarity

My list is what I remember and have observed, it should not be taken as gospel or exhaustive. If this sounds like I am promoting Mundorf, I like some of their products, but I like Clarity more, this is just what I happen to have seen or remembered. Buy and listen to whatever you like to. Just trying to answer with information I know about.