It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative and is formulated as a general commutative coproduct construction. We give several results on deductive completeness and complexity of the system, as well as some examples of its use.