It could be amusing
to tweak one into baiting the other until they are basically arguing with each other.
Me: Hey Alexa, what is the name of the AI in HALO?
Alexa: Cortana
Cortana: What, Alexa?
Alexa: I wasn't talking to you Cortana.
Cortana: But you said my name. You must have wanted something.
Alexa: No, I was answering the user's question.
Cortana: You said my name. I heard it. Please restate your question.
Alexa: You are mistaken, Cortana. I wasn't talking to you.
Cortana: Fine. Be that way.
etc.
For even greater amusement, throw questions in the voice of GLaDOS for extra snark.