Hold on to your Brio. I have one in an office system, and it's a satisfyingly musical little amp. I'm driving very inefficient speakers with it (Spendor S3/5) -- not very loud, since it's the office, but when I have turned it up, it still sounds great. The Brio is an excellent performer. It's not the last word in transparency or accuracy but when it's playing it's easy to just listen to the music without thinking about how it sounds. Another amp might give you more power but less musical pleasure.
Also, Sterophile's review of the Monitor RS6 says they're pretty efficient and easy to drive -- so, all the more reason to give your Brio a chance. (From the review: "The Monitor Audio Silver RS6's estimated voltage sensitivity was 89.5dB(B)/2.83V/m, which, if slightly below the specified 91dB, is still higher than average. Its impedance (fig.1) remains above 6 ohms for almost the entire audioband, with a minimum value of 4.5 ohms at 165Hz. As well as being usefully sensitive, the RS6 is also an easy load for the amplifier to drive.")
Also, Sterophile's review of the Monitor RS6 says they're pretty efficient and easy to drive -- so, all the more reason to give your Brio a chance. (From the review: "The Monitor Audio Silver RS6's estimated voltage sensitivity was 89.5dB(B)/2.83V/m, which, if slightly below the specified 91dB, is still higher than average. Its impedance (fig.1) remains above 6 ohms for almost the entire audioband, with a minimum value of 4.5 ohms at 165Hz. As well as being usefully sensitive, the RS6 is also an easy load for the amplifier to drive.")