If you're "passive bi-amping" with the speaker's cross-overs you're not going to have a significant power increase.
Both amplifiers are seeing the same signal. Their power supplies might sag a little less when feeding only one driver, although a couple volts out of 40 (~100W into 8 Ohm amp without the excess to account for diode drop) is only going to get you .5dB more before the amps clip at the same point. That may not even be audible and isn't going to sound like a volume increase.
If you removed the passive cross-overs and used an active XO you'd get a gain. If I had an 8Ohm speaker with 2.83VRMS signals for woofer and tweeter, with a passive cross-over I'd need an amp which could hit 8V peak rated at 4W into 8 Ohms. With an active cross-over I'd have two amps each producing 2.83 VRMS,4V peak,and rated at 1W into 8Ohms. Since the musical power spectrum favors low frequencies, it's not 2 x 100W = 400W. 120W + 80W active = 400W passive in an average 2-way.
Replacing the stock cross-overs with an off-the shelf unit is VERY unlikely to work. Most speaker designs achieve their cross-over slopes by combining the speakers' natural roll-off with a lesser electrical roll-off. Many have shelving filters for baffle-step correction, notch filters to tame resonant peaks, etc.
If you want to actively bi-amp, you'd need to measure the electrical transfer functions of the passive cross-overs, bypass them, and duplicate them using a DSP (Behringer has one for ~$300) or analog active cross-over which will produce the required slopes (you could populate Siegfried Linkwitz's 3-way ASP or 2-way + power amp Pluto boards for somewhat more).
Both amplifiers are seeing the same signal. Their power supplies might sag a little less when feeding only one driver, although a couple volts out of 40 (~100W into 8 Ohm amp without the excess to account for diode drop) is only going to get you .5dB more before the amps clip at the same point. That may not even be audible and isn't going to sound like a volume increase.
If you removed the passive cross-overs and used an active XO you'd get a gain. If I had an 8Ohm speaker with 2.83VRMS signals for woofer and tweeter, with a passive cross-over I'd need an amp which could hit 8V peak rated at 4W into 8 Ohms. With an active cross-over I'd have two amps each producing 2.83 VRMS,4V peak,and rated at 1W into 8Ohms. Since the musical power spectrum favors low frequencies, it's not 2 x 100W = 400W. 120W + 80W active = 400W passive in an average 2-way.
Replacing the stock cross-overs with an off-the shelf unit is VERY unlikely to work. Most speaker designs achieve their cross-over slopes by combining the speakers' natural roll-off with a lesser electrical roll-off. Many have shelving filters for baffle-step correction, notch filters to tame resonant peaks, etc.
If you want to actively bi-amp, you'd need to measure the electrical transfer functions of the passive cross-overs, bypass them, and duplicate them using a DSP (Behringer has one for ~$300) or analog active cross-over which will produce the required slopes (you could populate Siegfried Linkwitz's 3-way ASP or 2-way + power amp Pluto boards for somewhat more).