Robert, you get an A! :-)
To bring back more memories of English classes in days of yore, ‘will stay’ is a form of the intransitive verb ‘to stay.’ An intransitive verb does not take a direct object. ‘you’ is the object of the preposition ‘with.’ In this case, the prepositional phrase goes beneath the verb because it modifies the verb. Gosh, it all comes back, even to prehistoric days! Hey, Ushindi, I’m not THAT old!!
Even so, it’s a good cartoon, and it made me laugh for the right reasons.
I’m looking forward to taking it from the start. I’d never even seen this strip until about two years ago. This is much better than having it vanish!