Is there a way to come to enjoy more than 2 lines of results query preview per item on a google results page?
Yes and no.
First no you cannot alter how many lines of text appear for your site in the search results.
However...you can greatly enhance your listing by providing ancillary information on your site/business which can be included at Google's discretion which can greatly enhance your visibility. Some such items include:
These and others can all help to further differentiate your two line listing in the search results.