A floating, offshore drilling and/or production platform is equipped with a rail-mounted transport system that can be positioned at a plurality of selected positions over the well bay of the vessel. The transport system can move a drilling riser with a drilling riser tensioner system and a blowout preventer from one drilling location to another without removing them from the well bay of the vessel. Using the transport system, the drilling riser is lifted just clear of a first well head and positioned over an adjacent, second well head using guidelines. The transport system may then move the upper end of the drilling riser (together with its attached tensioner and BOP) to a second drilling location. A dummy wellhead may be provided on the seafloor in order to secure the lower end of the drilling riser without removing it from the sea while production risers are being installed.