Can I bi-amp my speakers with two different amps?

Hi Jokomo.

I have a pair of Cabasse speakers (from France), which have the mids/highs in one unit and the lows in a separate cabinet -- joined by an external crossover (with easy adjustments).  I'm driving the mid-highs with two Cary 805C monoblocks, and the lows with a VAC Renaissance 70/70 (two monoblocks on one chassis).  Pre-amp is a CJ ART.  Can't tell you how amazing ANY music (from any connected source) sounds.  And I listen to the system in my home office for hours on end, every day and night.  No fatigue ever.  Just can't wait to hear what pops up next on the playlist.

So the quick answer to your question is yes it can definitely be done using the connections described by others.  If you like the sound of your amps and speakers, you're going to be very happy.

Cheers.

I am also curious to try biamping  a pair of quality, 250 wpc+,  class D Monoblocks bi-wired into the Bass terminals of my older Tannoy FSMs.
I would use my Pass Labs XA25 for the upper half. 
Any product suggestions for an option under say $2,000?

68pete: I had two 20 amp circuits installed a few years ago for some Krell monoblocks that I have since parted with.  At least I have that part solved.

Do note that biamp arrangements can also hurt speaker coherence. I biamp my Coincident PRE's, but getting levels/frequencies properly balanced is a real challenge.  I probably should have invested in a quality microphone and done some real measurements to help with set-up. 

george and eric hit the important points - selecting the right amp for each and equalizing the gains.