Question: Some mates and I have the amount to cover the cost of an item but have a credit limit lower then the price. The purchase has a hard requirement that the payment method is a credit card. So, my mates and I put a negative balance on the card (I.E: The balance is 0 and then we pay something like 16,000 on it, making the balance -16,000 so we can make the large purchase putting the -16,000 balance back to 0).

Could we make the purchase using this method?

Answer: 
Most credit cards (at least here in the US) do have the concept of temporarily raising a credit limit for a purchase. It's always by request, and there's no guarantee of approval, so you would have to try and see. If the amount is grossly different from your current limit it will probably be a challenge unless your credit score and income have dramatically improved since they put your limit in place. 

If you can't get a limit increase, then as [Aganju](https://money.stackexchange.com/users/35405/aganju) suggested, finding a friend or family member with a high enough limit and giving them the money is probably a good bet.

I know I'd be happy to earn cash back for such a large fully-reimbursed purchase.

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One other thing I want to add. This purchase sounds.. somewhat sketchy. 

What merchant would pay credit processing fees on a high amount when a buyer is willing to pay cash/bank transfer? 

What merchant would be willing to accept a single credit card payment for such a high amount but not allow splitting among several cards (the per-transaction fixed fee would be negligible at high dollar amounts where the percentage-based fees would make up the bulk).
Typically, that does **not** work. Calling the bank might give you different info, but there is a risk that it won't work, even though the bank explicitly confirms it (happened to me, BoA). At the end, the original credit limit of the card applies, even if you overpay it with a million.

You can try to call and ask for a limit increase, even only temporarily; the risk with that is that your credit score might probably go down, and it might get declined, so you end up worse than before.

Also, once you transfer the money onto the credit card, it takes a lot longer to get it back. The official claim is typically '4-6 weeks', but it might work in 10 days if you are lucky.

My solution was to take out cash and hand it to a (personally and well-known!) friend, who had enough limit on her credit card and made the booking for me. The bank impressed only by being extraordinary disinformed, self-contradicting, helpless, and counterproductive.