Not as currently configured.  You would need to use the Amp and 3rd party speakers in place of the Beam in order to use a third party sub in a Home Theater setup. 

No.  If you were using an Amp to power front speakers, no soundbar, then you could use that amp to also power a 3rd party sub.  If you setup the amp as a 2nd Sonos room then grouped with your home theatre room, the connected sub output would be slightly delayed.

For completeness, if you used the amp to power rear surround speakers, instead of the play 1s. the sub output is turned off and still not usable.

I would look into using your amps in a different room, or sell, and get a sub mini.

Wow!  That kind of stinks.

I *can* use two amps to build a third-party surround system, but I *cannot* add just one Amp if I have a Bar or Beam.

I wonder why they do not allow this.  All Sonos gear.  Two Amps, no problem!  Buy their expensive Bar or Beam, and I'm out of luck!

You certainly can use an Amp as surrounds with a Beam.  However, the subwoofer out and line-in are disabled when configured as surrounds.