A method of elevating the deck area of a marine platform (e.g., oil and gas well drilling or production platform) utilizes a specially configured sleeve support to support the platform legs so that they can be cut. Once cut, rams or jacks elevate the platform above the cuts. The sleeve support is then connected (e.g., welded) to the platform leg and becomes part of the structural support for the platform. In one embodiment, two sleeves are employed. In another embodiment, the jacks or rams elevate in two stages including a first stage wherein one sleeve elevates and the other sleeve does not elevate and a second stage wherein both sleeves elevate together.