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Solid state amps into high impedance (16, 32 and more ohms) cabs - harmful?

Is it possible to run solid state amps into very high impedance cabs, like 16, 32 or even more? Is there something else going in the circuit then that could damage the amp, apart from serious drop of power?
 
I have an old Cerwin Vega power amp I use for a 2 channel headphone feed in the studio for tracking. I use it as a constant voltage source amp with series build-out resistors on the output, 1 per each headphone line in the booths and the large room.
It's over-kill, but works fine. I doubt it ever sees a load lower than 80 ohms.
 
[disclaimer, in case this is what the OP intended) I wouldn't run headphones off of the output of a power amp without understanding exactly what you are doing. The result is pretty hard on headphone.
 
I was thinking of pushing the power amp of my GK head harder by rewiring my current cab from 8 to 32 ohms (two 16 ohm speakers inside), after reading a thread about holy GK growl created by pushing the power section.

...but I just calculated I would drop the power from 125 to ca. 50 watts, so that's just 3-4 db difference. In my current band master volume on my amp is on 10 o'clock, we're really quiet for a rock band, so I don't think I would get where I want after all.... AND I like to push mids up high, so I'm audible no matter what volume I play.... :)

Thanks anyway!
 
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GK does some fun overdrive stuff with the output section on the RB series but I don't know if it happens on the way in or the way out with current or voltage. No harm in trying though.

There's a few doing similar with GenzBenz Streamliners. It gets the output overdrive into action nicely.
 
Maybe the OP has four 8 ohm cabs (or eight 4 ohm cabs!?!) and wants to run them all in series from the same amp. That's one solution to the "way too many cabs but only one amp" dilemma.
Interesting idea but would you really gain anything significant by such a drastic drop in output power?