There shouldn't be anything to stop you trying heavier gauge strings on your Variax.  You should notice some difference in tone in much the same way you would on a standard guitar. The difference in sound might not be as pronounced though, although for the acoustic models I think it should enhance the feel and the sound.  If you have a hard-tail 700 you should be reasonably OK as it is with maybe just a slight tweak to the truss rod to compensate for the greater string tension, but with the trem version you will also need to adjust the trem springs and maybe add another spring or two.

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  Line6Miller

I use 11-52 D'Addario Chomes (flatwound) with a plain .018 G string, gives a good acoustic sound & are light enough for string bending. See my thread "My solution to string imbalance problem"