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A problem for my SEO is a slight difference in British and American spelling for a major keyword, and also that it is searched for in both its singular and plural forms.
Can I try to solve the above problem by using somewhat different Meta title elements for each of these three files? Maybe even use synonyms for keywords there? Or is this something my site is likely to get penalized for?
I could also have small variations in the text of the headlines of three pages, as seen in the browser window, but that may be going too far, because normally such headlines would be identical. On the other hand I guess differences in the Meta keyword and description elements do not matter.
This is not a duplicate content problem, as I do not even aim at getting all three pages listed separately in the same SERP. (All are indexed now.)
I had a look on google to help you along the way (these are threads from WebmasterWorld on the subject UK vs US spelling [google.co.uk])
Regarding the plural version of your keywords, with Google stemming it shouldn't be a problem. Just make sure your keyword appears at least one in singular and once in plural in your web page copy.
Hope this helps
Leo