Can RBF be done by a third (or second) party
No, without knowing the private key it is not possible to create valid transaction and pay additional fee. There are some other complicated ways to force the transaction be included into a block, for example CPFP or creating non-final transaction ANYONE_CAN_PAY.

The simplest solution is seting the cost to 0.9998 BTC, user will pay 1.0 BTC with 0.0002 fee. This will produce the same result as in your example but without any additional actions.