Tri-Amping/Active Crossovers for Edgarhorn

I am thinking of tri-amping an Edgarhorn Titan system, to eliminate the colorations involved with the passive crossover network. It was recommended to me that using a single amp with the passive crossover should be sufficient, or at most I ought to consider bi-amping the woofer from the tweeter-midrange, and that tri-amping with a dedicated amp for the tweeter would just be unnecessary?

My concern is that even a simple capacitor 1st order filter for the tweeter could have a substantial sonic effect. ANy thoughts?
Drdna - do you already have your Titan's set up? If so, what specifically do you want to improve? Using two or three amps still requires some type of crossover. So this will not "eliminate the colorations involved with the passive crossover network." I agree that crossover components are very audible, but so are amplifiers. If you haven't already done so, suggest that you first set-up your Titans per Edgar's recommended configuration. Live with it for awhile, then decide what to do next.