OK, I figure I'll throw my two cents in here. But first let me say, the following is my experience and my opinion. I don't claim to be the God of all audiophiles with the Golden Ear that can hear the most subtle distortion known to man or Gods.
In my experience, Bi-Amping is fairly useless. I've tried it with several different speakers, mostly Sonus Faber, and found no improvement. As proof that Bi-Amping speakers with built in crossovers is less then useful I can simply look at all new Sonus Faber speakers. None of them come with the dual binding posts any more. In fact more and more the high end speaker manufacturers are going away from this.
Of course there is another approach similar to bi-amping called bi-wiring. In this case you run two sets of cables from one amp output to the HF and LF binding posts. Again, there are all sorts of debates about the pros and cons of this, but the net is that if it has any effect it is a very slight positive one.
The only time I've heard any noticeable improvement was on a set a speakers that a DIYer took out the crossover, designed an active crossover (that was inserted between the pre/pro and the amps) and the amps drove the speakers directly. In this case he was actually tri-amping and used different amps for each speaker. I believe the tweeter was driven by a 8W SET tube amp, the midrange was about an 80W tube amp as well, and the woofer was driven by a 300W Class D transistor amp. All three of which he built, along with building the 3 way active crossover. The original speakers were a pair of B&K 800's (I don't remember which model) that were floor standing 3-way speakers. They sounded pretty damn good before the modification, but they were amazing afterwards.
So after going through all this, here is the short answer. Rather then buy twice as many amps in order to bi-amp, I would spend my money on a better quality amp. Rather then spend my money on extra speaker cables, whether it's for bi-amping or bi-wiring, I would spend my money on better quality speaker cables. Oh BTW, I wouldn't spend a ton of money on speaker cables most of the high dollar stuff is just "snake oil".
Good Luck.
I don't think it's fair to lump-in bi-amping (as a concept) with bi-amping a set of speakers with a passive crossover already inside of them. The benefits of bi and even tri-amplification are well known and documented (many, many published papers in technical journals such as that of the Audio Engineering Society (AES) and many others).
Were it not for bi-amplification, the amount of power handling and lowered distortion products in modern commercial sound systems would be considerably worse than they are now. However, I agree that using active bi-amplification with a speaker already having a passive network in it is not quite the same thing as a commercial installation; in the latter, the only crossover networks that exist are indeed the eelctronic crossovers, which then send those signals to the amps that power the various drivers...and those drivers are absent passive crossovers. True, some may still incorporate capacitors as a stop-gap measure on their inputs (mid and HF drivers to be specific), that is, to help reduce the risk of driver damage that would otherwise result from setting a crossover point too low for a given driver. For example, suppose that in a three-way system, a mid driver was rated to handle down to 800 Hz, but a crossover is mistakenly set to 400 Hz - in this instance the driver is far more likely to sustain damage. An added benefit to active crossovers (and downstream amplifiers) is that the load presented to each amplifier is no more complex than that of the driver (and by complex, I don't mean arcane - I mean complex as in having a real and imaginary portion). Passive crossovers do in fact present a more complex load to the amplifier, but I suspect that most modern amplifiers can drive such a load with relative ease - the bigger issue is generally the power handling that some of the crossover components (in particular, dropping / tuning resistors) must dissipate.
Doing away with a passive crossover solves all of the problems associtated with them, but it does pre-suppose that the person setting up the crossover / amplifier / driver arrangement (just to echo XenonMan's comments) is well-versed in the subject matter; there's a layer of complexity that just doesn't exist (for the end user) when passive crossovers are utilized. That's not to say that for your project in question you can't learn and understand these principles of active crossovers - there is plenty of good reference material out there on the subject (see my post in the "Crossovers" thread that shows a link to a really good primer on the subject from Rane Corporation). You really should read that technical note - it is chock-full of useful and applicable information that would serve your project (or anyone wishing to understand crossover networks).
Nevertheless, active crossovers (I'll refer to them as such rather than bi-amped or tri-amped just to group them) are indeed vitally important as evidenced to the now-common practice of subwoofer use in HT systems. By using an active crossover (effectively, what comprises bass management), power handling and distortion products are improved, particularly in the staellites that, as a consequence of bass management (i.e. bi-amplification) would otherwise be tasked with reproducing regions of the spectrum that they really cannot do without introducing distortion due to exceeding their linear range of operation, and (worst case) their physical excursion and / or power handling limits.
I have to say though, every subwoofer system that I have ever implemented using bi-amplification (i.e. using the appropriate active filter network) has done wonders to lower the distortion products of the drivers reproducing things above the crossover point (i.e. 40, 50, 60 Hz...what have you) and to allow a better allocation of amplifier power. So, I don't think it's at all fair to say that bi-amplification does not improve matters - but it comes at a price (additional amplifiers, additional crossovers, etc), and in certain instances, I can see that little benefit (sonically) would be gained over a well-designed passive crossover - especially when used at moderate listening levels.
Also, to mdrconsult's point, bi-amplifying an existing speaker and still using its internal crossover passive complicates matters further still - because now you are introducing the magnitude and phase characteristics of the electronic crossover in addition to those of the passive crossover; I can see this as being very complicated owing to the interaction (with some very hit-or-miss results), that is, the added poles and zeros of the crossover network and all that entails, and again, to his point, this is why in commercial sound systems having electronic crossovers, there are no passive crossovers 'seen' by the power amplifiers driving each range of the spectrum - because the whole point of using electronic crossovers is to allow the tuning of the system to be determined by the electronic crossover settings.
As far as bi-wiring goes...well...in my
opinion I think that's not really necessary or sonically beneficial. If you look at the math behind such an approach (considering the speaker wire as a transmission line), there's nothing in the results that indicate any benefit whatsoever is realized. I know... "
them's fightin' words...", but I truly believe that the lion's share of fidelity lies in having drivers (and crossovers) that result in the most faithful reproduction of sound possible. Fundamentally, I see the exact same thing in microphones (and let's face it, both are transducers...just the opposite of one another), that is, you can take a poorly designed microphone and plug it into the best mixing console / recorder in the world, but you won't get the results that you would by plugging a great microphone into a garden variety board or recorder. Thus, I would rather have the best speakers (best sounding to me...whatever that may be) and have a decent amp than have a killer amplifier mated to some poorly designed and poor-sounding speakers.
As far as your question about sourcing one balanced signal to multiple differential (i.e. XLR) inputs, the best way to do that task would be to use a distribution amplifier. This device takes a signal in (pre-amp out) and provides multiple outputs of the same, and each one being its own independent circuit. You can find these (most commonly) as something like 2-in, 4-out, or 2-in, 8-out and so on. Check eBay, and if you need guidance with that aspect of your project, drop me a line.