Volume Control for second set of speakers

Nope, that won't work, you are switching power, not line level signals.   What would work, is to use the line level outputs from your amp, feed it into the volume control unit you found, and hook up another amp for speakers B.  

Not what you wanted to hear, I am sure.   But, that B output is speaker power level, so you can't apply line level electronics to it.   You could put a power resistor in series with each Speaker B, say 100W, 2 to 4 Ohm resistor, which will cut the volume a bit.   It will also affect the sound quality and not in a good way.  

Another option, which you probably don't want to hear, is using a set of speakers that are less sensitive than Speakers B.   

If your main amp is a home theater receiver, you should be able to control the volume to Speaker B in the settings menu.  

Thanks SpatialKing. Unfortunately my Integrated doesn’t have pre-outs. It’s a Yamaha A-S801. My first thought was to add a second integrated but it seems like I cannot  

I’m confused, why wouldn’t this monoprice box in the speaker wire run not work?

The A-S801 has record outs but, oddly, they are associated with specific inputs.

You can use that to drive a separate integrated.

For your consideration:

https://www.nilesaudio.com/product/tabletop-stereo-volume-control-selectable-impedance-magnification...
A perfect application for the TVC-1 is adjusting the volume of
remotely located speakers. The TVC-1 adjusts the volume of
speakers connected to it by attenuating the amplifier signal.
Niles volume controls use autoformers instead of L-pads for
the volume controlling element. This assures minimal internal
power dissipation with virtually no power wasted as heat.