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: 
In contrast to @ChrisInEdmonton's credit card, my credit\* card does allow such charging. It does have additional spending limits per purchase/per day etc, so I'd probably have to ask my bank to raise the limits for the foreseen transaction. 

\* I'm in Germany, and my credit card (like many credit cards over here) look from the outside (e.g. the store where I do a purchase) like a credit card but internally work mostly like a debit card with a comparatively small credit.
I'm not really clear why you don't just use a Visa Debit card for this purchase? I use Visa Debit for expensive purchases like long-haul international flights, hotels and health spas or whatever. It's really easy - I just transfer $12k or so into that account and then start spending. You can just put your $16k onto a Debit card and pay that way.

There are no monthly fees, and best of all, it is still backed by Visa just like a credit card. What I mean by that is, recently I was travelling around Europe and a dodgy vendor charged my card for 200 Euros that I didn't spend. The vendor didn't respond to my emails, so I complained to Visa and they reversed the payment. So you're just as safe using a Visa Debit as a credit card, and I never get stuck paying interest or late fees because I never owe Visa money. Debit cards are the best - I haven't owned a credit card in years.