By the looks of your pic, even with the EICAS covered up, I would say that travelling at Mach.84, or 517 mph ground speed, is probably as fast as the aircraft will go at 32,000 ft.
It took me a while, and with a lot of help from other members here, to realize that you can not fly by speed alone. You need to balance other requirements such as alitude, weight, and weather. For a given air speed the higher you go the faster your ground speed will be.
To show you how the Mach number, air speed, ground speed, and altitude work together try this.
Set you AP to 250 KIAS and your alitude to say 40,000.
Take off and engage the autopilot, and autothrottle. Sit back and enjoy the view. Keep an eye on your mach number.
Once the aircraft reaches 250 KIAS your airspeed will remain steady. But look at the Mach number on the bottom of the scale. It will be slowly increasing as you climb. Also, if you are flying the same aircraft as you have shown in the pic, you will notice a series of yellow and red lines on the right side of the speed indicator. The yelow lines are a warning that yopu are close to going overspeed and the red ones indicate the maximum air speed the aircraft can safely fly. These lines will adjust up and down, again depending on your altitude.
If you want to progress even further use the concorde, set your airspeed to 350 and your altitude hold to 58,000
As you climb you will pass mach 1 and come close to mach 2 without touching your throttles.
Yes you can take the concorde through mach 1 without using your afterburners is FS2004.
For a more indepth discussion go to this thread. It explains in great detail almost exactly what you are experiencing.
http://www.simviation.com/cgi-bin/yabb/YaBB.cgi?board=COF;action=display;num=1107887786Hope this helps
P.S. Beefhole....did I get it right? ;D