True bi-amping bypasses the internal crossovers so you must modify the speaker internally. You must use an external electronic crossover of which there are few analog ones ( I have used the X-Kits for main/sub) or go digital like the MiniDSP. PA crossovers like DBX and Berhringer are not HI-FI devices.
Running two amps to the two sets of binding posts on a commercial speaker is doing nothing. Nothing as it does not bypass the crossovers. Just as bogus as bi-wire. Any rumor's that dedicating amplifier frequencies have any difference is just more snake oil. If you can afford two amps, just buy a better amp and it will make an audible difference.
Sub to mains, yea electronic as the physical size and cost of a 80 Hz or so passive crossover is insane. Never mind a 20 Hz high pass to the sub. HP to the mains can make quite a difference in moderate and above distortion but is best done low level.
Mid to tweeter is where it matters. DSP allows very accurate time, phase, and eq. for any response in your room you want. Folks like Linkwitz much favored it especially with dealing with open baffles. Then again, folks like Dick Small say a competent engineer can do just fine with a passive. As I build my own speakers, I can tinker with the crossover to get it pretty good in my room. It may not be in your room so the DSP side may win there. A MiniDSP can do a lot of things that PC based software does not.
But, there are always buts, If feeding analog into a MiniDSP, you have additional A2D converters and DACs that are not exactly state of the art etc. You really need to understand measurement and psychoacoustics to know what the target needs ot be for you. Understanding DIRAC or even REW takes quite a bit of work. I think you can bet a MiniDSP USB in and PCM to external DACs out but that can raise all the same "which clock" issues as any PCM output does.
Active analog, like the X-Kits, don't have any eq. More efficient and the crossover is not impacted by the dynamics of the speaker loads and impedance. Very clean if you pick the right op-amp, but can cause turn on and off thumps if you don't handle that elsewhere. I do not know of another true high end active crossover. Bryson?
Passive is reliable, but hard to mass produce for everyone so eq needed externally. (I use JRiver) Problem is, even speakers costing several thousand dollars frequently have terrible crossovers a second grader could do better. There is zero excuse for a commercial speaker not to have a Kipple measured response within 2 dB across the BW and phase alignment within 20 or so degrees at crossover. If I can do it on a ladder in my back yard, so can big companies. Focal, Revel, Sonas Faber, Elac, and Dynaudio, are a few who do pretty well. How companies like B&W or Klipsch can be so horrible I do not know.
An odd one left is passive line level. I do this to my mains on my desktop using an appropriate size cap depending on amplifier input impedance, ( .22u in this case) to give a first order HP. Going above first order is impractical and risks distortion of the inductors. First order is almost always not steep enough for mid to woofer. I use it to take the load off my 4 inch desktops driven by a 2W amp. If trying for a second order, you can get into serious preamp impedance load issues. As I have built amplifiers and studied Self, Cordell, Leach etc, I know how to modify an amp input stage for a second order and can even modify the feedback compensation for further specific eq. Not easy unless you are an engineer. ( LtSPICE is wonderful)
I see suggestions on matching amps for range. Well, in the days of crappy amps, maybe but we can buy very very good amps now pretty cheap. Do consider how you may effect the sound by amps of different gain.
