power & time align

It depends what you mean by different power/volume.

Just turning up the system doesn’t require any modification to the system setup. Even without changing anything the level and hence power is continuously changing; that is the nature of audio.

Theoretically it can be argued that Thiele/Small parameters are a small signal parameter and will change at high power levels, but there is not much that can be done about modifying the cabinet tuning.

If the relative levels between different frequency bands of a PA system are changed, the effective crossover point will move and that will slightly affect the alignment. For example, Say the system has been aligned with a bass to mid crossover point at say 100Hz, with a filter slope of 12dB per octave. If the bass section is then turned up 12db the bass and mid bands will overlap by an octave, which could mess up any time/phase alignment between the frequency bands.

If your intention is to set up the dsp/crossover to optimise the response of your system, it can be done at reasonably low levels. Measuring outside (assuming no reflective walls) will minimise anomalies caused by reflections and room resonances. Once set leave the crossover alone and make any subjective adjustments prior to the crossover. I know that some people like to mess with the crossover mid gig, but if you do that there is not much point in time aligning the system. I say time aligning, because the alignment is done by using the delay function. When measuring use the phase response curves to align the system.