As mentioned DBS might be unique in offering a charge limit. However, there are a couple ways you can effectively add a charge limit to another credit card:
1. Use a supplementary credit card. These generally have hard charge limits. For example, if you have a spouse/partner then you can "cross-issue" supplementary credit cards: you use his/hers, and vice versa. The primary cardholder can set a sublimit on the supplementary card within his/her credit limit.
2. Use a rechargeable wallet, such as GrabPay, then make your purchases using this wallet. This works rather well with the UOB Absolute American Express credit card as an example, or so I'm led to believe.
You can. I can vouch for that on behalf of a family member's recent direct experience. It's up to the bank and its proprietary credit authorization decisions, but there's no regulatory or legal barrier as far as I'm aware. If it weren't possible they wouldn't have overlimit fees in their price schedules, but they do — and they're very happy to levy them when the occasions occur. It's a good source of revenue/profit.
UOB's overlimit fee is S$40. OCBC evidently doesn't have a separate flat fee but
does add a 3% uplift based on the balance, at least in certain circumstances. The credit limit may only indirectly affect the charge limit based on whatever proprietary credit authorization algorithms the bank uses. A charge limit, on the other hand, is a hard stop.
So why have a credit limit, you might wonder. And the answer to that, for most banks anyway, is that it provides high confidence to the cardholder that charges within the credit limit will be routinely approved. But it doesn't necessarily constrain the bank. If the bank considers the cardholder to be a good credit risk at that moment (yes, often) then the bank may be very happy to approve the charge(s) above the limit — and collect the extra tribute.
Anyway, net net there's no guarantee a lower credit limit will be binding on the bank. A particular charge limit would be.