Based on my experience, the limit is not based on the score itself, but on the report.
The credit score would determine if you fall into the range of scores they accept to consider the application.
But your credit report is what they look at to see what your other current limits are, to see your balances, and determine if you fit their profile of cardmembers. So if you have 5 cards and 2 are $500 and 3 are $1000, they are most likely going to give you around $1000, perhaps $2500. They don't like to overextend credit to someone who hasn't shown responsibility with high credit lines.
But if you have cards around 10-15k, most of your new cards you apply for should be $5k min and some may even pass the $15k - just depends on who you are applying with. BUT, that said, too many hard inquiries can also affect the credlit line they offer you, because it raises flags. So that's why you would garden in between application sprees, so your new accounts can age and the hard inquiries become older than 6mo to a year, so that your new applications have better chances of not only being approved but also to get the credit limits you're looking for.
