After reading this question What stops other benders from mastering the four elements? While it seems that it would break one of the rules of the show, that only the avatar can master all four elements. There would also be good reasons as to why someone couldn't learn all four, there is always the opposing element that is hardest for the Avatar to learn. I don't see any reason why someone couldn't learn to bend two elements (not master, but just bend since Thadeus's Answer What stops other benders from mastering the four elements? to the previous question is apparently the Definitive Answer on the subject.)
Many benders do learn to bend beyond their element such as Toph becoming a metal bender and Katarra bending blood. Now metal is considered part of the Earth but so is sand and it seems that sand is moved more like water. Iroh was able to adapt a water bender technique to fire bending which means it is possible to learn and use different bending styles. Also Iroh spent time connecting to the spirit world and that seems to be the main reason the Avatar is able to bend all 4 elements. So if someone was connected to the spirit world or even their past life that would fulfill that requirement.
Would it be possible to bend two elements? There do seem to be times where it has been done in the series such as bending mud which is both Earth and Water. And there would definitely be limits such as a Earth bender couldn't bend Air and a Water bender couldn't bend Fire. But why couldn't a Fire Bender learn to bend Air. They both use breath control as a main focus of their bending. It also states on the Energybending wiki entry that all bending used to be done as an inner bending but that it became element bending.
So with new bending techniques being formed all the time, already stated used of combined elements being used, an assumed spiritual connection to a past life or a spiritual journey been taken, energybending rediscovered is it possible that two elements could be bent by one bender who is not the Avatar?