I see this all too often. An SEO neophyte gets a particular web page to the top of Google for a high volume and well converting search term, then they get greedy and the go after other search terms for the same page. In short, they fiddle.
This fiddling may include adding more keywords to the title tag, adding lots more new keyword-rich copy to the page and building backlinks with a wide range of different anchor text.
Not a good idea.
You see by being greedy and trying to get one page to rank for multiple terms all you succeed in doing is confusing Google.
Think of the Google ranking algorithm as being like the mental process we use when browsing in a bookshop.
Say for example, you walk into the bookshop looking for a book about Australian Labradoodles.
On the book shelves you see three identical books, the only thing different are the titles.
Australian Labradoodles, Australian Terriers and Border Collies
Australian Labradoodles – the ultimate guide
Dogs, Horses, Australian Labradoodles and other domesticated animals
Which one would you pick up and why? Check your answer here: X
Sure, by all means go after other search terms. But make sure you create new pages for those new search terms. Don’t be keyword-greedy and if it ain’t broke, don’t fix it.