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).
You can possibly find a prepaid credit card. This is a card (in the USA, generally Visa or MasterCard) which looks to the merchant like a credit card, but from your viewpoint is one where you deposit money in advance, and any charges are debited against your existing credit. I have never used one, but if they work logically you should be able to deposit 16,000 of whatever currency you use, then charge that amount. Here's one list of potential vendors: <https://usa.visa.com/pay-with-visa/find-card/get-prepaid-card>