I searched but couldn't find anything about this. I've heard some bassists like Victor Wooten, John Myung etc. use an amp for bass and a separate amp for the treble from their bass so they can play high and low notes simultaneously and the treble won't become distorted. Anyone have any ideas on how to do this?
In theory, if you use a large 500W Bass amp with a large speaker cabnet (like that one with a single 21" speaker in it) with a good 100W guitar amp hooked up to a Bass speaker cabnet with lots of little speakers it could work, giving you a rich full sound.
How would I connect those together to work together? Would I need a mixing board or something or would it be something to do with the outputs being connected or something?
Actually, most efect pedals have a sterio output, their outputs are the exact thing, but to keep it "lowest common denominator" they have it labled "amp" and "mixer". And both outputs still work when the effect is bipased.

Either that or you can always make a splitter. The parts will be AT MOST 7$. 10$ if you pay someone to make it for you.
Some amps come with a built in crossover, or you can get external ones. Basically, you choose a frequency (just for this example I'll use 100Hz). The crossover will send all you notes below 100Hz to the bass speaker (usually a 15" or 18") and all your notes above 100Hz to your treble speakers. (usually 10" and horns)

GK also have a HMS system where they have a 700w power section that powers your woofers (10" 12" 15" or whatever speakers you use) and a 50w power section that powers your horn. This is so the horn doesn't distort.

So it's not so much that you use different amps, it's more that you'd use different cabs.
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you can buy a bi amp. carvin's upper line of bass amps are bi amped. i have one, one half is to my 4x10, and the other is to my 18. you can bi amp it, or single amp it. it sounds very nice. a bi amp would be a better option for you, being the cheapest way.
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Which would be better: putting my bass through an amp, then a passive crossover, then putting the two signals through a guitar and bass amp or biamping them?

I'm guesing I could use effects on the guitar amp and separate ones on the bass amp if I used a passive crossover?

A good site I found about biamping: [http://sound.westhost.com/bi-amp.htm]