Hi Big Rich,
You have confused the maximum what a speaker "can handle" with what it needs to drive it to high enough sound levels to satisfy the listener. These Polk Signature S55 are sensitive enough (90dB at 1 watt) to reach 110 dB when 10 feet away, when only driving the two of them at 125 watts. A sound level of 110 dB is beyond uncomfortably loud, and into Jet Engine territory causing ear damage with long exposures.
Pushing them with 140 watts instead of 125 only increases the sound by 0.5 dB which is virtually insignificant. (By the way, 200 watts only gets you 2 dB more than 125 watts.) Clipping can be obtained in almost any system, but can be avoided if one listens to the sound output and backs the volume off as soon as they start to hear any distortion.
How big a room are you using, and how far away from your speakers will you be sitting? Are the speakers away from the walls or near them or in a corner?
So IMHO you probably won't need the second amplifier. Your best bet will be to get a good Sub. It will help unload the Signature S55s of the most power hungry portion of the sound => Bass.