Is there such a device that can take an already-amplified signal from that 10W amp and boost it out on the other end

A device that will amplify something that's already amplified? I don't know of anything that'll do that in the indoor-stereo realm.

There are some car amplifiers that'll take speaker-level inputs as well as line-level inputs. But those don't re-amplify the speaker level inputs. They just convert the speaker level inputs back down to line level, then feed that into the normal signal chain of the amplifier.

I don't know of any home-stereo amplification gear that'll take speaker-level inputs. Maybe it exists, I just don't know of any.

Doesn't that X10 system offer a receiver-end with line-level outputs so you can hook up just a plain old stereo amp (something with bass and treble) to it?