EDIT: Sorry Seth, I deleted that which you quoted in the above post, and reposted it with the required corrections and explanations here in this post, as I realized from your post #11 that some of what I had said did not apply to ALL receivers.
You forget, most receivers will not allow surround sound to be used when A+B are engaged. So when you want to use the surround channels you will either lose the tweeters or the lower range drivers on the front left and right, which is unacceptable in most if not all setups.
Actually, this depends upon the receiver's design. With some receivers, the "B" speakers DO represent and utilize the separate surround rear amplifiers, but these receivers do not specifically allow assignment of the surround rear amplifiers to bi-amp duty, although they CAN be used as such. As I explained, the "B" outputs on most receivers do not utilize any of the other channels' amplifiers, and instead simply represent an extra set of (usually parallel) binding posts from the front R/L amps. I incorrectly assumed that this is the way ALL receiver's "B" binding posts operate, which was an incorrect assumption, as some receiver's "B" binding posts DO represent completely different amplifiers than the front R/L amplifiers as they utilize the 6th and 7th surround rear amplifiers for the "B" speakers.
What I was describing was two different applications when using a receiver whose "B" binding posts simply represent another parallel set of binding posts from the front R/L channel amplifiers. One involves using the "B" binding posts of this receiver to connect another set of speakers (alters the impedance seen by the front channel amps) to the R/L front channel amplifiers or to facilitate easier bi-wiring (does not alter the impedance seen by the front channel amps) to the R/L front channel amplifiers. The other involves assigning the unused (in a 5.1 setup) 6th and 7th channel surround rear amplifiers of this receiver for bi-amp duty. This second application does NOT utilize the "B" binding posts at all, but instead utilizes the 2 pairs of surround rear speaker binding posts. These two applications, the use of the "B" binding posts of a receiver whose "B" binding posts simply represent another parallel set of binding posts from the front R/L channel amplifiers, and the use of the unused 6th and 7th amplifiers of a receiver for bi-amping are two completely different applications. In the first scenario, provided we are talking about a receiver whose "B" binding posts simply represent another parallel set of binding posts from the front R/L channel amplifiers, when using the front channels' "B" binding posts, the extra set of speakers or the bi-wired speakers can easily be run while the receiver is in multichannel mode, whether the receiver is set up for 5.1, 6.1, or 7.1. With the other scenario, as long as the unused surround rear amplifiers are assigned properly to bi-amp duty, they can also be easily utilized in multichannel mode, but obviously only in 5.1.
I apologize for assuming that all receivers' "B" binding posts simply represent another parallel set of binding posts from the front R/L channel amplifiers. This IS the case with most receivers, but after doing a little research I have discovered that some receivers' "B" binding posts DO indeed represent different amplifiers than the front R/L channel amplifiers and instead represent the 6th and 7th surround rear amplifiers. These receivers obviously do NOT allow the use of the 6th and 7th channel amplifiers for surround rear duty simultaneously with the "B" speakers.
So there is a difference in terminology between receivers. Many receivers allow the 6th and 7th surround rear amplifiers to be used to independently drive another pair of speakers in another room. On most receivers, this is called "Zone2" and is assignable as such in the receiver's setup proceedure. These two amplifiers can also often be assigned as bi-amping amplifiers in the receiver's setup proceedure. Some receivers, however, do not call these speakers "Zone2" but instead simply call these speakers "B" speakers. The "B" binding posts of these receivers represent the 6ht and 7th surroud rear amplifiers and can be utilized to independently drive another set of speakers in the same exact way as "Zone2" speakers would be driven. And they, too, can implicitly be used for bi-amping, although this may not be described as a use for them in the user's manual. In a receiver whose surround rear channel amplifiers can be assigned to what is called "Zone2", the "B'" outputs refer to an extra set of (usually) parallel binding posts off of the same 2 front R/L channel amplifiers as the "A" binding posts, and not independent binding posts representing the 2 surround rear amplifiers. With either "type" of receiver, you can't utilize the 6th and 7th amplifiers as surround rear channel amps when they're being used either for bi-amping or to independently drive another set of speakers.
So I guess, in hindsight, I should have clarified in my previous posts that what I was describing were receivers whose "B" binding posts represent an extra set of (usually) parallel binding post off of the same 2 front channel R/L amplifiers as the "A" binding posts, and not receivers whose "B" binding posts represent independent binding posts of off the surround rear R/L channel amplifiers.
Sorry for the confusion.
BTW, on your RX-V559, the "B" binding posts do simply represent an extra set of binding posts off of the same 2 front R/L amplifiers as the front "A" binding posts. And to add further confusion, these "B" binding posts on your receiver can be assigned as "Front" or as "ZoneB". However, because they represent binding posts off of the same front channel amplifiers as the "A" binding posts, when assigned as "ZoneB" they can not be utilized to playback independent input source material to what is being played back in the main zone via the "A" speakers. Your receiver also has "Zone2" capability, which does allow independent input souce material to be played in "Zone2", but external amplification must be utilized in order to set up a "Zone2".