Your phrase "Raise the volume" made me giggle. When I was new in the recording studio I would ask the engineer to turn up the bass, turn up the drums, turn up the trumpet, etc. One time after long session he snapped at me, I can't keep turning everything up, there's only so much "up" available, you have to tell me to turn something down!
Your question reminded me of that because in audio electronics we don't actually "raise the volume," we almost always "attenuate" the level down from the fixed gain level that is set by the all the amplifiers in the system. So when we "turn up the volume," we are actually turning down the attenuation to let more of the already amplified signal come through. Gain and attenuation are little bit strange concepts for non-techies but valuable to understand as it affects the overall noise of the system.
My take is that any volume controls on sources early in the signal chain should be adjusted to get best sound quality and lowest noise. This usually means leaving all the digital volume controls set at max output to avoid loss of resolution that is typical of digital attenuation, and also turning up any analog "output level" trim knobs on analog source components to maximum, or at least turned up to match other fixed output components. Save the adjustable attenuation main volume control for the end of the signal chain with the preamp just before power amp, or the integrated amp last step before speakers. By using analog attenuation close to the end of the chain, the noise accumulated by all the preceding components in the chain will also be attenuated along with the signal itself. This is the traditional audiophile setup.
The latest trend for our advanced colleagues is to run 64 bit digital volume control at the beginning of the signal chain, as part of the player software, like Roon or JRiver, then send that losslessly attenuated high resolution digital signal to the DAC playing full scale into the power amp. Simple and elegant, with very low noise and lots of magic software buttons to tweak.