I'm #2. Leave alone or change things to get to #1?

Personally, I wouldn't do anything else to that page. If you are #2 for your desired term, start going after other related terms using other pages. A bit of personal history: I once had a personal site that I was able to get to #3 for a relatively competitive term (Note - that definition is completely subjective based on your personal interpretation of "relatively competitive"). Being the type of person I am, I was absolutely determined to get #1. To make a long story short, up until the day I sold the site, I was never able to rank any higher than #7 for the same term. I learned from that mistake and hope you will as well. I should have just left it alone.