How many open credit card accounts do issuers like to see (according to some formula or rulebook) when someone applies for a new credit card? Specifically when each card is in good standing and paid down very low?
It isn't the number of cards that is important.
They care about your score which lets them estimate your risk.
They care about your income, because that lets them calculate the maximum amount of debt you can support
They care about how much debt you have and how much it costs each month to carry that debt.
They care about the type of debt. A mortgage debt of $100K and credit card debt of $100K are very different.
they also care about the age of the accounts. Too many new accounts make them nervous.
If you have X credit cards, and you have a good score, and your income can cover the additional credit then they are likely to approve another card.
In some cases it is easier to ask for a bigger credit limit on an existing card. Though if you are seeking an additional card for the benefits then upping the credit limit will not meet your needs.
Some companies have multiple cards with different mixes of benefits, so it can be possible to switch card types within the same bank and not impact your credit score.