Another, easier case question:
Obviously, of the two variants
This looks like him
This looks like he
the first seems more naturally idiomatic. However, is it grammatically correct?
I think the not-necessarily-separable questions at work here are:
Whether "to look like" is a linking verb in English ("This looks [~to be] he") (likely it is);
Whether "to look like" is an idiographic construction following its own rules, or rather an ellipticization or reduction of, say "This looks like [it is] he" or "This looks like he [looks (/does)]."
...The only doubt in my mind about whether "This looks like he" is correct is the Columbia Guide citation here, which argues:
Than is both a subordinating conjunction, as in She is wiser than I am, and a preposition, as in She is wiser than me. As subject of the clause introduced by the conjunction than, the pronoun must be nominative, and as object of the preposition than, the following pronoun must be in the objective case. Since the following verb am is often dropped or “understood,” we regularly hear than I and than me.
Is there a linguistic basis for the Columbia Guide's assertion, as there clearly is for the alternative? Or is this simply an argument between prescriptivism, realism, and second-wave prescriptivism?
Cf. "He plays like I" "I do it better than she"