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
Yes your speakers very much so have major liabilities being that old and not rebuilt most everything is limited 
capacitorsfor sure wear out ,and most likely  real crap 
electrolytics in there which should not even be there resistors also .  Which just  this alone would totally rob the system of fidelity and dynamics . If the amp too is old  rebuild it capacitors , resistors 
wiring ,all can be be drastically improved 20 years ,even 15 years capacitors are known to leak ,or dry out  . I have been through 
this in the past ? First decide do you want solid state ,or Vacuum Tube, that will determine  how efficient your Loudspeakers need to be ,and how Loudin SPL levels you need ,and room size how far away you sit.  How powerful the Bass , or maybe a great monitor 
with excellent subwoofer-s.  Many options , your $$ budget will 
determine this ,how about preamp, or integrated ?
Well, then this brings up the question as to which speaker manufacturers are known for employing the best quality electronic components such as capacitors, resisters, etc.?  Only interested in big, floor standing speakers here.  Yes, I want the big, open, dynamic sound, but I also want great vocal tonality and timbre of instruments.
Amp output goes to the speaker.  That portion which generates heat is lost to compression.  To one degree or another, it's always present.
@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