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Yes! After doing a little internet research I found that, generally, a substance containing both hydrogen bonds and lone pairs can potentially experience autoprotolysis. For example, ammonia and acetic acid can both experience autoprotolysis.
There are numerous examples of autoprotolysis other than H20, since autoprotolysis is the proton transfer between two of the same molecules. An example would be acetic acid: CH3COOH <------> CH3COO- + CH3COOH2+. In addition, the Keq would likely be very very small, favoring the reactants, since they would be the most stable.
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