Meaning of "That, and other things"?

Hello everyone. I am reading a novel, and I came across this expression. Could you please let me know its meaning?

Once we crossed Broadway, though, all she did was slip her arm into mine and say she couldn’t wait for our Oban.

“You’re becoming an alcoholic under my influence.”

“That, and other things,” she said. I thought she was referring to her growing fondness for Eric Rohmer and didn’t bother asking her to explain. Then it occurred to me she might have meant something else, but for fear of finding it out, I didn’t press her to explain.

- André Aciman, Eight White Nights, Fifth Night

This is a novel published in the United States of America in 2010. This novel is narrated by the nameless male protagonist who meets Clara at a Christmas party in Manhattan. Now the protagonist is at the movie theatre with Clara.

In this part, I wonder what the underlined expression means.

Would that mean that she is becoming an alcoholic, and plus, some other existence (perhaps a fan of Rohmer films) because of him?

Or would it mean that she is becoming an alcoholic, because of the protagonist's influence, yes, but there were other influences too that made her an alcoholic...?

Thank you very much for your help.