I have no debt except for one credit card that I pay off every month, and I've been in that state for years, but my credit score won't go past the mid 700s. I actually tried prepaying my credit card one month so that my debt to credit ratio would be zero, but that made my score drop. It's called a "thin file", meaning they don't have enough data to tell if I'm a risk.

your credit score benefits from having a history of managing more than one line of credit. it's debatable how much opening a bunch of credit cards helps with this (in the short term, it actually hurts). ideally you would have a mix of credit cards, a mortgage, and some other type of debt, all of which paid off on time.

it's only a moderate impact factor though. having an extremely long history of on-time payments and low overall utilization can still get you an excellent credit score. it just takes longer.

You should have at least 2 credit cards, and not both with the same bank, of course.

I had two credit cards with Chase (and an Amex with BoA) when Chase decided that I had died.

If it wasn't for the Amex, I would have had some big problems!