Another way of reasoning.?

All allegories, both religious and secular, exist for this purpose.

Your reasoning changes when your mind changes.Not only is it possible for another way of reasoning to exist but such reasoning already exists in the world.In the mind of a genius.

Einsteins theory of relativity if just one of many examples of unorthodoxed reasoning by man.

the laws of logic do not change. reasoning has a basic structure. reasoning is what it is unhangeably, as it definition is the foundation and really basic of all inquiry and conclusion making. there is higher level of knowledge, but not l\higher level of reason. the highest reason you can reach is the most basic foundaiton of rationality. however, most people never make it to this core reasoning, and they rely on flawed rationality which is quite sad indeed