In my book I have: if we have bring or take sth with ... we use a personal pronoun and not a reflexive pronoun after the preposition. Is have in this list too?
I can only lend you ten dollars. It's all that I have with .....
I'm not a teacher, but I think it's possible to use have sth with you (and also have sth on you with the same meaning).
For example: I don't have much money with me / on me.