My 2 cents is that you're thinking way too much about SEO. It's fine to target a specific set of keywords with a new article if the article is also relevant to your site and useful to users. But don't break up articles just for SEO reasons when one page could easily have housed all of the article's content, and don't worry about going after different kw's with different *parts* of an article. You'll make yourself crazy. Bad ROI too.
If the article is genuinely too long to be convenient for the user, or if it really does seem to contain what naturally break into three or four parts, then fine. Otherwise, don't sweat it down to that level of detail. Do another article instead. :)