I agree with pkvintage. I currently triamp in an active stereo system and definitely hear the difference. I have removed the passive crossovers in my speakers.
In the past, with same speakers and tube amp I now use for midrange/tweeter, I tried biamping out of the preamp as you suggest, with a large ss amp for bass. Didn't like it at all.
BTW, in a setup as you describe all amps reproduce the full bandwidth, so not a good solution. In this case a bigger amp is generally better.