Intuitionistic logic is a form of logic that doesn't have the law of the excluded middle, or LEM. The LEM says basically that a proposition that is not true is false, and a proposition that is not false is true. Classical logic has LEM but intuitionistic logic does not.
A 3-value logic is a logic where a proposition can be not merely True or False, but also something else, typically Unknown. It can be used to handle various propositions that 2-value logic cannot, propositions formed such that there is no consistent way to assign either true or false to them. Naturally, LEM also does not apply to a 3-value logic. I tend to view LEM as a device for defining what counts as a proposition. In a logic with LEM, for example, you can't allow a proposition like the Liar, "This sentence is false", so it just can't be formulated as a proposition, but in 3-valued logic it would be possible to allow it.
It occurs to me that Intuitionistic logic is a sort of stub 3-value logic, one where there is no way to deal with the third value, but where the possibility of a 3rd value is still allowed for. That is, without LEM, there is no way to prove that a proposition can only have one of two values.
Are there any developments of this idea in the literature? For example, is there any work where intuitionistic logic is used as a base for either classical logic or 3-value logic just by adding axioms or other features?