What is the ruling on changing the intention of making up an 'Isha prayer to performing the current night's 'Isha prayer after having started the prayer?

It is not permissible to change one's intention during prayer from one obligatory prayer to another, because the prayer from which one transitioned becomes invalid, and the prayer to which one transitioned is not valid because it was not intended from the beginning. Ibn Uthaymeen said: "If one transitions with an intention from one obligatory prayer to another, both become invalid." Therefore, both prayers must be re-offered, starting with the one that was missed first.