In "I scheduled a meeting for you and me to chat," should I replace "me" with "I"?

My first intuition is that it should be:

I scheduled a meeting for you and I to chat.

But then I noticed that I would use "me" in:

Patrick scheduled a meeting for you and me.

and

Patrick scheduled a meeting for me to chat with him.

I think the reason I'm struggling is that in the first sentence, I cannot tell whether "you and I" plays the role of an object (for whom the meeting is scheduled) or the subject (who is chatting).

Solution 1:

It's "you and me", not "you and I". You are using "to chat" as an adverbial infinitive here. Think of how it sounds by replacing "you and me" with "us" versus "you and I" with "we".

I scheduled a meeting for us in order to have a chat.
I scheduled a meeting for us to chat.

This looks and sounds fine, with or without the implied "in order to have".

I scheduled a meeting for we in order to have a chat.
I scheduled a meeting for we to chat.

This looks and sounds awful, with or without the implied "in order to have".

Solution 2:

The test is to consider a sentence with just the pronoun in question. "I scheduled a meeting for me to chat" or "I scheduled a meeting for I to chat"? While the pronoun appears to be the subject of "to chat", it's also the object of "for", and "to chat" is not a finite verb form, and so doesn't take a subject in the same way that finite forms do.

Compare to other nonfinite verb forms, e.g. "I saw him walking down the street" versus "I saw he walking down the street". Although the pronoun denotes the person performing the action of walking, and so it might seem that the subjective pronoun is called for, the pronoun is also the object of the verb "saw", and it is the latter factor that dominates, resulting in an objective pronoun.