So I have a site with domain name following this format: keywords for keyword keywords.com and it ranks #1 for that and that phrase search has the most traffic. But if i google my website as keywords as keyword for keyword keywords or some variation that is less competitive it rank in the top 100 if you just take out the s when searching. I figured google would just exclude the s, but I guess not. Any advice in general as to how I can get around that without having to optimize three different sets of keywords with/without the s?
Google considers both each individual word and the phrase as a whole. So for the plural version it sees that your domain name is an exact match. It does not know if your site is directly related to the singular version of that phrase. So you need to show that your are relevant for that phrase too. The easiest way to do that is to build some links using that link anchor text. Go submit some articles, do some blog commenting or do some social bookmarking. It should be fairly easy for your site to get rankings for that phrase as well.
Plural and singular keywords are two different keywords. The only way to rank is to build quality links for them. Use variation in your anchor texts.
Combining or swapping to optimize each one of them can be a solution. Or you can just choose which one is easier to rank on. I am sure there is one from them that is not that competitive. If both are competitive, optimize them both.