Do you look more like me . . . or do you look more like I? The case of a pronoun following this kind of comparative structure, typically at the end of a sentence, depends on who or what is being compared.
If you write “My sister looks more like our father than I,” for example, one would assume that the “I” implies “I do.” But you wouldn’t fault someone for thinking you mean your sister looks more like your father than like you. This is often a source of confusion, so it’s best to reword for clarity. If the point is whether the sister looks more like the father, the pronoun should be objective (me, not I): my sister looks more like our father than she looks like me.
Instead of writing “My sister looks more like our father than me,” I might rewrite “My sister looks more like our father than like me.” That pretty much eliminates the problem. And if you add the word do to that first example, you won’t have any confusion either: “”My sister looks more like our father than I do.”