Great question to ask at the end of your conversation, but please DON'T ask this if you didn't solve the original request.
True Story: I called my bank last week to solve an issue I had at the ATM. The CSR needed my account information, which I couldn't access at the time. I offered my company name but he said he couldn't help. Then he said, "is there anything else I can help with you today?"
Now, you all know I'm pretty easy going, but this question right after saying he couldn't help made me furious.
Don't make your customers furious. Only offer additional service if you have indeed offered service.