I don't see what the crossover has to do with any of it really as it's just a filter for the hz mainly...
I know you can't change the ohm load of the A speaker itself but when you connect two or more speakers together then the ohm load changes and affects the draw from the amplifier.
Consider the example of an 8 ohm speaker that has one woofer, one tweeter, is not bi-wired or bi-amped, and has a simple first order crossover consisting of a capacitor in series with the tweeter, and an inductor (coil) in series with the woofer.
At high frequencies (well above the crossover frequency), from the amplifier's perspective the woofer will essentially not be there, because the high frequencies are blocked by the inductor. At low frequencies, the tweeter essentially will not be there, because the low frequencies are blocked by the capacitor. So at any given frequency (outside of the region of the crossover frequency), the amplifier is seeing only one driver, either the woofer or the tweeter.
Therefore the nominally 8 ohm speaker will have a nominally 8 ohm woofer and a nominally 8 ohm tweeter.
Wiring two complete 8 ohm speakers in parallel does indeed result in a 4 ohm load, but that is because each complete speaker is an 8 ohm load (nominally) at all frequencies.
If you take that 8 ohm 2-way speaker and bi-wire it, nothing changes as far as the load impedance seen by the amplifier is concerned. What changes is that the series capacitor and series inductor restrict high frequency currents to flowing only in the wires to the tweeter, and low frequency currents to flowing only in the wires to the woofer. One advantage that has is that back-emf generated by the woofer will be kept away from the tweeter, and more generally, unwanted interactions between highs and lows may be reduced.
If you bi-amp that same speaker, the amp driving the woofer will see (nominally!) an 8 ohm impedance for low frequencies, and a very high impedance (i.e., a negligible load) at high frequencies, due to the series combination of inductor and woofer. The amp driving the tweeter will see (nominally!) an 8 ohm impedance for high frequencies, and a very high impedance for low frequencies, due to the series combination of tweeter and capacitor. As Bob indicated, that can be determined more precisely if the impedance vs. frequency curve of the speaker is known, as well as the crossover frequency or frequencies, and the rolloff characteristics of the crossover network.
Regards,
-- Al