How should the pronoun agreement in this sentence be changed, if at all? Katherine and Jon spent the entire day preparing theirselves for the big debate.

The appropriate reflexive pronoun is Themselves as it is used when the subject and the object of the sentence are the same thing. In this example "Katherine and Jon" and "themselves" are equivalent or related terms.

The change in the sentence should be themselves instead of theirselves

Explanation:

This sentence uses a reflexive pronoun, which is a kind of pronoun that we use when the person that does the action of the verb is also the one who receives this action, it is a very common way of expressing many common activities since it may be applied in different situations, besides the correct spelling is themselves using the root word them as the object pronoun not their as the possessive adjective.