Who do you think I am?

Teo1. Who do you think I am?

2. Whom do you think me?

I think #1 is correct. According to Treasure of English Grammar (written by Liu Yi), #2 is also acceptable. Do you agree?

# 2 is totally foreign to my ear.

Changing the pronoun may clarify:

2. Whom do you think me?

=> e.g.

3. Do you think me him?

(But quite peculiar, as Philip suggests.)

MrP

3. Whom do you think me to be?

Is the above sentence acceptable?

sitifan3. Whom do you think me to be?

Is the above sentence acceptable?

It's grammatically correct, but not very colloquial. Again, I think that "who do you think I am?" is the best.

the verb/subject agreement is easily identified by the original statement: "Who do you think I am?" while the later additions tend to mix the verb and subject syntax so that they become jumbled.