Bi amping with two different pairs of monoblocks

Instead of this method of bi-amping that you are considering, how about a different "bi-amping" approach that might yield as good if not better results?

You don’t mention in your post if you have any subwoofers but here is an alternative approach, given that your Triode TRX M845 tube monos have a low damping factor relative solid state and thus controlling bass drivers is not their forte (but musicality is is - in particular - the midrange):

High-pass the signal out of your preamp at, say 80 Hz, and let your tube amps and main speakers handle everything from 80 Hz and up.

Tap the lineout from your preamp and send it to two very good subwoofers that take care of the duties from 80 Hz and down.

This way you’re using the DSP in high-quality subwoofers paired with their solid-state amplifiers, and designated woofers for the bass, which should yield you a better and tighter bass response. You also have more freedom in where you place your subs to get a more even frequency response throughout your listening room.

So, instead of spending money on the second set of monoblocks for your mid and high frequencies, spend the money on high-quality subwoofers instead.

Yes, your main speakers are very good but they can’t touch the bass reach and response of high-quality subwoofers, not least since the subwoofers will be powered by solid-state amps with a significantly better ability to control the drivers than what tube amps can.

@knotscott

 Every case is different.  I don’t agree that it’s a ridiculous proposition.  It depends on several variables. 

I said it was a ridiculous proposition in the context that the OP would be better served buying a decent front end and some high quality speaker jumpers, they really make a difference.

When mixing brands your answer is maybe.  Physical it’s possible, but you probably won’t get the synergy you’re looking for. The biggest obstacle is that every  company has a specific sound and finding two companies that sound the same isn’t going to be easy, especially with there being less and less brick and mortars willing to lend equipment.

All the best.

I find this thread interesting as I'm about to embark upon a biamping expedition myself. I have two beautifully refurbished Yamaha m2s. I plan on building a electronic crossover with burson op-amp replacements. This crossover will cross over at the mid-base mid-range crossover point of 400 cycles which is exactly what my speakers use. That way the amps will work in their sweet spots, my preamp is an anthem str and will automatically cross over to the crossover to the two amps running my founder 100s and to my sub xr13. I think the external crossover is the answer to this problem for the original poster. Someone mentioned a Dayton DSP which I believe is just a rebranded mini DSP which would do the trick because it would create a crossover point. Allow you to adjust the timing and allow you to adjust the levels for each amplifier that has a good chance of succeeding. If each amp has level controls this is definitely a must try. All the people that say this is a fruitless proposition. Forget that as audio files everything we do is a an experiment in our constant search for audio perfection. No experiment is fruitless if it increases the knowledge that you have about reproducing sound in modern systems, that is just the journey that we take. I've been doing this since I was 16 and could drive myself to my local audio store and set up a friendship that lasted through my teenage years. Go ahead and hook them up. And balance them and see where you stand. You can always unhook them and go back to the old way. Try them forwards and backwards. You never know what you're going to hear. Have fun! 

@lordmelton 
I said it was a ridiculous proposition in the context that the OP would be better served buying a decent front end and some high quality speaker jumpers, they really make a difference.

 Got it.