The output level will depend upon the input level and the amplifier's gain and the 'taper' of its volume control attenuator potentiometer. If you use a source with higher output voltage, you may be able to get more power out -- but whether you need it or not will depend on your speakers' sensitivity, your room, the source material (music) and your ears.
It's worth noting that the power output meters (which I assume your amp has) are typically voltmeters; they measure the output voltage level and "do the math" to convert volts to watts according to Ohm's Law and assuming a fixed load impedance (typically 8 ohms). The power level measured by the meters isn't accurate in any real sense unless the amp is driving a load of fixed impedance (e.g., an 8 ohm power resistor). Even then, the meter may not measure "true RMS" AC voltage, so it's best viewed as a light show, or at best an index of the output level. These meters are basically useless except as cosmetic adornment.
The loudness control function you describe sounds like the traditional Yamaha variable loudness, EDIT but calibrated
backwards relative to most Yamaha variable loudness controls (see image below). The idea is to set the volume control to your maximum listening level, then use the loudness control to turn the sound level
down as needed. The Yamaha loudness control approximates the Fletcher-Munson loudness perception curves, so that the apparent frequency balance is maintained as the sound output level is decreased. Many, many Yamaha hifi products featured this -- as, by the way, did numerous hifi manufacturers in the 1950s and early 1960s (EICO and Sherwood, to name two examples).
YamahaCR-2020loudnesscurves by
Mark Hardy, on Flickr