@Goliath
Just imagine that the total amount of power available to all of the channels in a receiver is a "bucket". All of the channels have to share from that one "bucket" of power. But each individual channel can only take a maximum of half of that "bucket" at any one time. No individual channel can take the entire "bucket" all for itself.
In the case of your 706 receiver, the "bucket" is 200 Watts of power. Any individual channel can dip into that "bucket" at any given moment and take as much as 100 Watts of power all for itself, but no more.
But do remember that the total "bucket" is only 200 Watts. So any two channels go dip into that "bucket" and take 100 Watts each, but then all of the remaining channels would get zero Watts and would have to be silent.
So let's imagine that 5 channels all want some power at the same time. All 5 of those channels would dip into the "bucket" of 200 Watts. Obviously, if all of those 5 channels get at least SOME power, they can't ALL dip in and get 100 Watts. The "bucket" just isn't that big!
If they all grabbed an equal amount of power from the "bucket", each of those 5 channels would get 40 Watts. Or it could be the case that 1 out of those 5 channels needs to play louder than the rest. So maybe 1 channel grabs 80 Watts, while the rest get 30 Watts each. Or maybe 1 out of the 5 channels needs to play as loud as it possibly can. So it grabs the maximum that any 1 channel can take, which is 100 Watts, leaving the other 100 Watts in the "bucket" for the remaining channels to share - so maybe the other 4 channels each grab 25 Watts.
Now, if you were to give 2 out of those 5 channels their own, separate amplifiers, now you only have 3 out of the 5 channels dipping into that "bucket" of 200 Watts at any given time.
So, once again, maybe 2 out of the 3 channels each grab 100 Watts, leaving zero Watts for the 3rd channel. Or maybe all 3 each grab an equal amount of power, so each of the 3 channels would get 66.66 Watts.
You can see in that example: when the receiver was powering all 5 of the channels, if all of the channels dipped into the "bucket" and took an equal amount of power, each channel only got 40 Watts. But now, with 2 out of the 5 channels having their own, separate amps, each of the 3 remaining channels can grab 66.66 Watts. So, in that way, using a separate amp to power some of the speakers increases the amount of power that remains for the other channels that are still being powered by the receiver.
But continuing, maybe 1 out of the 3 remaining channels grabs as much power as it can from the "bucket". So 1 channel takes 100 Watts, leaving 100 Watts for the other 2 channels to share - so each of them could take 50 Watts, for example.
Again, remember back to when all 5 channels were being powered by the receiver. If 1 out of the 5 took as much power as it could - 100 Watts - each of the remaining channels only got 25 Watts. Now, with 2 out of the 5 channels on separate amplification, 1 channel takes the max that it can from the receiver - 100 Watts - and the other 2 remaining channels can have 50 Watts each, instead of 25.
So you've got the "bucket" of 200 Watts no matter what. It's just a matter of how many channels are all dipping into that "bucket" and taking some of that power for themselves. When you add a separate amp, now you have fewer channels dipping into that "bucket". But at any given time, the most any individual channel can take out of that "bucket" is 100 Watts.
Hope that helps!