Multi-Line Text Box vs Single Line Text Box

We have a 'Notes' section in several of our webpages that is currently only displayed as a single line text box. We tend to get short responses (5-7 words) describing what they need. This almost always results in the need for a follow up before any action can be taken.

Would providing a Multi-Line text box lead the user to believe that we were looking for a more robust (see: lengthy) response? I'm basing this solely on intuition so if there is any research for or against this thought I'd love to know about it.