To not overload a room yet still have some bottom end at lower volume
without destroying it at moderate volume.
Can it be done and if so through speakers alone or does it take a combination
of equipment to get that sound and still retain the mids and highs.
Am I asking too much or is it just way outside my budget to even try.
Don
You are dealing with the results of the ear's non-linearity. That old Fletcher-Munson curve:
https://www.grooveboxstudios.com/fletcher-munson-curve/Achieving the same musical satisfaction/enjoyment over a broad range of listening levels, say 70dB peaks to 105dB peaks, using the same loudspeaker is simply not gonna happen.
There are reasons why good recording studios employ several pairs of speakers during mix down. It is essential that a final mix "translates" well on different speaker types at different listening levels. You don't use the same monitors to mix chamber music and gangster rap or metal.
The most cost effective method to meet your challenges is to get a great pair of small monitor speakers and team them up with a capable, high quality subwoofer that will allow varying the low pass/high pass turnover point between about 60Hz to 200Hz. At very low listening levels one may want a 200Hz crossover point to fatten up the upper bass low midrange that the non-linearity dictates for fullness, but at higher levels that fattening up will result in bloated, muddy low frequencies. At higher levels, the 60 Hz crossover point will sound more "right".
Getting musical reproduction to sound "right" is a complex soup of listening level, speaker type, content input, crossover points, room dimensions, driver diameter, number and type of LF drivers and on and on.
Bottom line is we never get it "right", only "right-ish".
Given your unique requirements I heartily recommend a monitor/subwoofer or a speaker with separately powered and adjustable low frequency components. There is a plethora of options out there. Step 1: find a monitor or small speaker that gets the midrange right. Music is by and large a midrange event. Make sure the highs aren't in your face. Too much detail often is an indicator of a bump in the lower treble. Next, try subwoofers that are adaptable like I mentioned. Ask the monitor speaker builder what he/she recommends. Make sure you have return privileges on the sub. Getting a sub that blends well with smaller speakers demands a speaker with exceptional impulse response... the infamous "fast" sounding drivers.
Two things to remember:
If you can hear the sub, it is too loud.
Friends don't let friends buy Focal or B&W? Just sayin'.
The smaller speaker builders off the best performance/investment values.