They all have a limit. Even on mine if I breach around $150k in any month I get a call kindly asking to pay it down or provide financial information to apply for extended credit. I'm not in the business of giving out my personal financial details unless absolutely necessary, so I choose to just pay down and it immediately opens up.

Like I said - they want to see extended use of the card at high spend levels. One off spikes, expenditure not typical of your noted income level, or no financial filings to back up your earnings/expedniture its unlikely they'll extend credit. Though I'm not sure why you wouldn't qualify in general. Continue spending, make sure don't miss payments, have high FICO score (I understand this is the measure in the US) and be prepared to prove income. I recall having to prove my income at the time. I can't 100% recall but I think that I showed my P60 for prior year, which in the UK is an official statement of annual earnings from my employer (shows income and taxes paid). Certainly UK Amex wants to see that [income] at a sufficient level. I think also showing a current account with steady income (e.g. employer/business) and sustained cash level of say $100k+ will make them more comfortable. The issue is why would anyone keep more than a few k in a current account, so you probably need to show savings accounts with accessible cash if not the former.