A bank manager explained their approach as follows.
Start with your gross income, deduct income tax and HECS (if applicable) to get to your net income. Come back to this later.
Add all your credit limits together. Calculate 3% of those total limits. (I'm this scenario, the bank assumes a 'worst case' of you maxing out every credit card you have, and having to make the minimum repayment on each one, assumed to be 3% of the total balance - which could be up to the total limit.) Take this 3% figure away from your net income.
Consider any other minimum repayments on other financial products like a home loan. Take that away from your net income.
Then come the 'cost of living' expenses that you often get asked about - rates, utilities, insurance, groceries, blah blah blah. Take these away from your net income.
If the number is still positive, continue processing the application. Take the customer's desired credit limit, calculate 3% (per the previous process), and take that away from your net income.
If the number is still positive, consider the other undisclosed lending criteria (including margin between the 'number' you're now at and zero, knowing that spending will increase over time), credit report data etc etc, to provide an outcome.
If the number after considering the credit limit is negative, consider whether a lower limit can be offered (which may include being approved for a lower level product) - then repeat the other considerations above.
Basically, banks have to be able to ensure that you can afford the repayments on the credit product you're applying for. Nobody says you have to afford the statement balance on a card - just that by getting this new product, paying the minimum required isn't going to cause financial distress etc. Case in point, got approved just this week for a 10th concurrent credit card. The 'number' of open cards isn't such a big issue versus combined total credit limits, number of credit enquiries and repayment history. (An advantage of having so many and paying them all on time is you have just about every bank noting every month how great you are at paying things on time, which has a very positive effect on your credit file.) I'll generally apply for a new one every 3-6 months, and close cards when they're no longer useful to avoid having toooooo many.
Not financial advice, blah blah, just some interesting things learned from people in the know.