Undesired Pages Ranking for Desired Keywords—What Should I Do?

I’m managing a fairly large site, and while it ranks for the keywords I want, some pages that rank aren’t really ideal for those keywords. I think I could create better content on a new page specifically targeting these keywords.

So, my question is: Should I just redesign the current pages that are ranking, or should I create entirely new pages focused on these keywords and see how they perform?

Additionally, there are some pages I don’t want to change, but I’d still like to target the keywords they’re ranking for more effectively on a new page. Any advice?