https://en.wikipedia.org/wiki/American_Foursquare

If you read the definition of an American Foursquare, IMO this is not close to a Foursquare. No stairs, no porch, no dormer, not tall enough. I'm not sure your home has a definable style and it's got a definite problem with visual balance and appeal.

I agree the roofline is somewhat different, but prior to the additions, the home would have had a square profile and the porch could have been cast off in previous years, so it made me wonder. Would you feel comfortable commenting on the stylistic elements you do see and directions we could possibly take it? Or ways to begin investigating? I see what appears to be some Craftsman trim in the interior (around doors and windows and in floor moldings) but not too much that would lead me in that direction either.