Because my tone preferences seem to be achieved by using lower volume settings on my basses, I usually need more wattage than most players, i.e., I never play with volume settings (on my basses) at 100%. I've had both the Rumble 200 (preferred tone) and the 500-plus Rumble extension cabs for both. Both were "close" to being enough volume and punch for my tastes, but just not quite enough. I'm sincerely hoping that these new Rumbles will be just that "little bit more" oooomph. But, as I said in my previous post, I will definitely wait to see if they put out style and dimension-matching cabs as well.
You don't need more wattage, that comes from the power amp section of your bass head. You need more pre-amp gain, because when you use lower volume settings on your instruments you are, of course, lowering the signal level from your instrument that is feeding your bass head. I'm going to conjecture that you are using a passive style bass (no battery powered preamp in the bass itself).
On a passive style bass, the volume pots (controls) definitely do affect the "tone" of the instrument as you turn the volume knob down. The non-technical explanation is this happens because the elements (bass, treble, volume, etc.) of a passive tone circuit mutually interact with each other. So when you change any one of those elements such as the volume control on your instrument, for example, it also affects the bass, mid and treble tone as well. This is why some (certainly not all) bassists prefer active basses where the tone controls are electronically buffered from each other and from the volume control so the various controls on the instrument don't interact with one another.
There are advantages and disadvantages to both active and passive instruments. For example, if you had an active bass, then theoretically, lowering the volume knob on your active instrument would not have the effect you desire on your bass tone.
Acquiring a more powerful head will not solve your problem since the tone change you experience and desire from lowering your instrument volume control is, of course, also knocking down the signal level your bass head has to work with. Specifically, the preamp section of your bass head needs more signal level to fully utilize the capabilities of the power amp section of your head.
Using a boost pedal of the kind usually employed to drive the preamp section of an amp head into distortion should solve your problem. Just don't use so much boost that you drive the pre-amp into distortion, that's all. Use just enough boost on the pedal to make up for the drop in signal level caused by turning down the volume knob on your instrument. You will then have both the tone and touch sensitivity your looking for and the full volume capability of your bass head. Some of these boost pedals are highly sophisticated even incorporating vacuum tubes in their circuits. That may not be necessary to get what your looking for, but some of the pedals out there will definitely work better for bass than others. A compressor pedal will also give you make-up gain.
If your going direct into a PA, be sure to talk to the sound guy about how you lower the volume control on your bass, and why. Good luck with that.
Edit: I assume you know how to run your bass head, i.e., you know the difference between input gain and master volume. Your problem may just be that you are not using enough input gain to compensate for the lowered volume settings you employ on your bass. Note: You must exercise caution not to accidentally over-drive your bass head no matter how you decide to get the extra gain you need. You may wish to take some time and do a little reading on "gain structure" on the web.