Your credit score looks pretty good. What I did is applied for every card they sent me and my credit score got better and my limit raised. I don’t use but two tho.
They might raise your credit limit if you stay with them and make monthly payments. Amex and Discover Card are generally very picky, just give yourself more time to build more credit history and they might send you applications in the mail eventually. Credit card companies will pull up peoples credit history from time to time to see who they want to do business with.
We are octogenarians who have limited income now but an excellent payment record with our credit card company. We started with a credit line of $ 5K some years ago. and are now at $ 17K. We even had it raised temporarily to $25K so we could purchase a car on the weekend. So apparently the CC company does have faith in us for such a regular limit.
What’s an upgrade? A bigger debt hole to jump down into? If your credit score is 724 you should already have some pretty darned good cards, no annual fee, etc.