The biggest difficulty with this idea is that from the moment the narrator calls a character me/I/myself, the reader will see the character and the narrator as the same person, and they won't stop seeing it that way unless you start a new chapter that refers to a different character in the first person (and are very careful to do this without making the reader get confused between the two narrators).
When the narrator and a character are the same person, it is unnatural for the narrator to talk about things that character will never find out about.
I thought he was insane. Jason remained stoic. He was remembering something terrible that had happened to him at school, but at the time I had no idea what mad train of thought was driving through his head; I only learned this later when I stole his diary to tear out the page about me and Kylie.
"Is everything alright?" I asked.
"Didn't the narrator tell you," said Jason, his expression unreadable, "I'm not the
"You don't understand," I said. "I am the narrator. I won't know what you're thinking now until I steal your diary in chapter six."
If you don't want the narrator to be the character, then the character has to be he/she, not I.