That depends, if we are talking about an AVR or multi-channel amp, then power supply voltage and current capabilities are a constraint... if one channel uses up the available current from the shared PSU, then the other channel(s) will be constrained (lose power) due to insufficient "power" from the PSU.
Monoblocks of course, don't suffer from this, and the issue often gets worse as you increase the number of channels within a component - which is why it is most obvious on high channel count AVR's.
Often the benefits of biamping relate to bypassing the limitations of the power supply in one amp, by using a seperate amp with its own power supply...