AMEX allows you to overpay your account.

However, there is a undisclosed maximum payment amount but you can issue multiple payments.

So what I do when I anticipate a large payment is perform binary search to find the maximum since the amount is validated in the front-end (I suppose I can peak at the source but binary search is faster!) and issue a split payment. Then I repeat for the remaining amount.

For example, if I want to pay $100 but the limit is set to $60. I would issue a payment of $60 and another payment for $40.

I just like to keep my balance down so I pay off large transactions as soon as I can.