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How many new accounts do you have? When was each account opened?
I would try another lender. Your last late was almost 2 years ago. Do you still have that account opened? Has it been paid on time since then? If so, I would contact the company and try a goodwill effort and ask about removing the negative mark.
You have 44 new accounts? How long has the oldest one been open?
You mentioned that one of your denial reasons was too many new accounts in the past year. How many accounts have you opened?
Lenders advise against opening new credit when going for a mortgage because it's adding to your debt. Also, the adjustment from the changes in your average age of accounts scoring and could lower your score. You also take a slight hit when the new account reports and sometimes it can take a couple of months to get back the points you lost.