[Q] How does crossovers effect impendance / power distrubition among the multi way speaker system?

hope everyone havin a good day.

Lets say we have an amp that outputs 20watts per channel and we want maximum amount of bass possible with the speakers mentioned below:

there is gonna be 2 big fullrange drivers and 2 tiny fullrange ones that are gonna be crossed over to create a bass roll off @ around 100 or 200hz. in a no crossover situation when we wire these to give a reasonable nominal impendance we either give both big and small spkrs 5 watts each which is not so good for the max bass output we want.

my question is does blocking the bass from the small ones with a cap (which would raise impendance @ those blocked freqs in the small ones) causes the bass to be lost or simply those bass freqs that small ones reject gonna be forwarded to the big ones?
 
The amplifier will give all the bass to the woofers. It doesn't change if you give more to the fullrangers.. except the amplifier will be overloaded. You can make it produce too much, and if you do you may break it.

Think about it in terms that the whole drive Voltage will be seen by anything connected to the amp directly. It is not a case of distributing the power (Watts).
 
No.

If you connect one speaker to the amplifier it gives you some level of sound.

Now, if you connect a second speaker to the amplifier, the first one produces the same level. It doesn't change.

All that happens is that your amplifier needs to supply more current.
 
It wouldn't lower the bass, no, unless they were out of phase 😉

It's not going to help much to use so many woofers, and your amplifier won't like it. When you cross the fullrangers at 200Hz, this means the woofers are working on their own below 200Hz, which is usually what you want.