So are there up to three options here assuming you have 2 x 2 channel amps:
- bi amp; one amp on tweeters, the other on mid/bass
- bi amp; one amp on left speaker (left channel on tweeter, right channel on mid/bass) and the other amp on right speaker. This may only be possible with a pre-amp and 4 mono blocks depending on the inputs/outputs available.
- bridge the amps so you have a more powerful amp on each channel; left and right. Obviously only an option if you can bridge the amps.
Dealing with the last one first, I once heard a setup which sounded very "loud". It was very "in yer face" compared to the non-bridged setup and would be very tiring for me. Each setup will be different of course.
The first option is the more favoured, since the delicacy of the higher frequencies won't get drowned or drained by the power hungry lower frequencies
However the second option may work very well depending on the design of the amp and connections available, if the power supply (which is now dealing only with half the mid/bass demand) can provide that extra big of power that's on tap without sacrificing the detail of the higher frequencies on the other channel. In practice I'm not sure what the connectivity would like if there's an integrated amp in the equation.
My advice would be to audition a bridged setup since I suspect you'll other love of hate the result. And then go with the hig/low frequency split but try both if at all possible and go with what you like the best.