That’s the behavior of the simple text editor (TextEdit) in OS X.
You can modify a Cornell notes template by adding additional rows in advance.
If you Google ‘Cornell notes’ you will find a variety of samples out there, including at least one that provides multiple rows with lines separating them.
Or you can create your own Cornell notes template in another word processor such as Pages, Word, etc. If you use Pages, it will have the advantage of displaying well in your database, and (if you have Pages on an iOS device), you can also work with such notes on your iPad or iPhone.
Aside: Many years ago, when I was an undergraduate in college, I assiduously underlined or highlighted almost everything I studied in my textbooks and class handouts. Yes, I made A’s, and that is indeed something of an aid in studying. But that approach doesn’t work, of course, when one goes to the library and is reading references - librarians frown on that sort of thing. One learns to take notes, instead.
That was a long time ago. I graduated from high school in 1947, the year Walt Mossberg was born (but for years, he’s looked older than me). In my college undergraduate years there were no computers or scanners, no Xerox machines, no Web or DEVONthink.
Doing library research taught me something very important. To retain information for future study and review, the best approach is to summarize important points in my own words in my notes. I began to change my habits in studying my course textbooks and class handouts, as well. About midway in the first semester of my sophomore year, that change shows up in one of my old college text books. The first several chapters were heaily underlined and highlighted. The remaining chapters are unblemished, because I had switched to keeping a notebook for summarizing and commenting on the information content.
That’s the premise of Cornell notes, that longterm retention of infomation is better served by learning to summarize or excerpt important information in notes, than by vandalizing the original source material. That mental exercise is the important component of this approach, whether or not one uses the simple format of Cornell notes.
Nowadays, my main database that I use for research and writing contains tens of thousands of reference documents and thousands of my own notes. Those original references contain no highlighting or other marks. Indeed, I shudder at the thought of inflicting such blemishes on them. I would no sooner mark them up than use a highlighter on an original copy of the Gutenberg Bible or an Audubon print. 
I use rich text notes, and make heavy use of links to references and other notes. Some of these notes use the Cornell Notes format when that’s appropriate, others (in fact, the majority) do not.
I find highlighting or other markings on my references distracting, and often actually impediments to taking a fresh look at a reference. If, for example, highlighting had been added when one is examining a reference from a particular perspective, it can be a hindrance to looking at that same reference from a different perspective. Of course, adding highlighting druring the first reading of a document can become really misleading if one didn’t properly grok the information - it would be more drudgery to remove bad highlighting than to revise or update a note. As always, these are my personal perspectives; feel free to disagree.