From Thomas Grano, my sometime companion in the world of nominative conjoined objects (NomConjObjs), this catch:
At the end of three weeks, I finally called the chair of the search committee and invited he and his wife to go out to dinner with us. [in "They're here!", 7/24/12 Chronicle of Higher Education blog post by Lesboprof, available here]
That’s a 3sg pronoun in the first conjunct, in a direct object that’s the notional subject of an infinitive — the first example with this combination of factors that I’ve seen.
NomConjObjs are much more common with 1sg pronouns than with 3sg, and much more common in second conjuncts than in first; the configuration 2nd conjunct + 1sg is far and away the most common one, as in between you and I (which has become virtually a formula). These are so common that I long ago stopped collecting them.
But the configuration 1st conjunct + 3sg is much rarer. I have 11 examples in my files, including Grano’s find and this one from Mitt Romney, reported by Mark Liberman in LLog in January:
I like he and Callista.
(coordinate) objects functioning as the notional subject of a following VP — a likely context for nominative case, since the cooordinate NP “feels” subject-like to many speakers, even more likely in a coordinate object, where nominative case is now widespread.
These are of several types, including the type I’ve coded as DI: direct object + infinitival VP. I have 3 of those in my files, including Grano’s. The other two:
… my daughter just decided this year she wants she and I to volunteer to go and answer phones… (Morning Edition Sunday, 9/11/05, Sunday Puzzle segment, listener Chad Graham (of St. Louis) talking)
Would you like Opal and I to go and get the car and come back for you? (Elizabeth Daingerfield Zwicky to Paul Armstrong, in conversation 0/18/07)
No doubt more of these are out there.