Crossover considerations for biamping?

I'm looking to build a TMW setup and am considering biamping it between the MT and W for flexibility and giggles (not interested in active crossover). MT would just be a normal crossover, but my question is, do I need to make any special consideration on the high-pass circuit for the MT and the low-pass for the W with a full range signal to both circuits?

My initial thought was that, in a full range, the signal gets 'divided' up between the M, W, and T, so every part of the signal has a place to go. If I were to biamp it and send a full range signal to both the W and MT circuits, the low end on the MT wouldn't have a dedicated W to handle the low end of the signal like it would in a MWT. Would I need to beef up my components to handle what would otherwise be the 'W' part of the signal since it doesn't actually have a W to handle that part of the incoming signal?
 
my question is, do I need to make any special consideration on the high-pass circuit for the MT and the low-pass for the W with a full range signal to both circuits?
You must apply low pass filter for woofer. For the mid/high a high pass filter will help lower the distortion and make them sound cleaner.
Would I need to beef up my components to handle what would otherwise be the 'W' part of the signal since it doesn't actually have a W to handle that part of the incoming signal?
A high pass filter is the answer.
 
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