Yes, this is possible, but a second application is assessed against your total existing obligations, including the outstanding balance and minimum payments on your first card, as part of the overall debt-burden ratio calculation. A strong, consistent repayment history on your existing card can work in your favour, while a high utilization or any recent missed payments on the first card can make approval for a second card more difficult, regardless of your income level.
Check your own exact figures with the Credit Card Finder - free, in under a minute, no sign-up required.