I’m with Hank on this, you need to be going back to your client and explaining what brand identity is all about. If you do not have the knowledge or experience do this, you should’t really be offering professional services In this area.
Frankly if I had a client who insisted on this kind of thing, I’d walk away and politely tell them that I would be wasting their money and my time. They don’t want professional help, they want someone to realise their own ego. You will, almost certainly, hear that they were great at art in school at some point in the conversation. ‘I wanted to be a designer’ ‘I’m quite good, you know’ etc etc.