With biamping you have vertical and horizontal, assuming 2ch amps. Horizontal would be one amp powering the highs and the other powering the lows of each speaker (each amp supplying portions of both speakers). Vertical would be one channel of one amp powering the highs and the other the lows of each speaker (amp supplying one speaker). With vertical, the channels aren't load balanced, but each of the amps sees the same total load. With horizontal, each amp has a somewhat matched load on each channel, but one amp will likely be working harder powering the lows. Though also generally you don't need as powerful of an amp to drive the highs.
The reason it isn't recommended doing this with a receiver is because all of the channels share the same power supply. With separate amps, the channels from each amp have their own supply to draw from which means no "competition" for that power. So while you are biamping, you are techincally just playing games with how the power is allocated.
Then you have monoblocks which would be a power supply dedicated to that channel
If you are looking to augment power, just about any decent external amp will have more real world power than any receiver.