Offshore locations present significant amounts of wave energy and free sea space, which could facilitate the deployment of larger numbers of wave energy converters (WECs) in comparison with nearshore regions. The present study aims to find a suitable design for an offshore floating version of CECO, a sloped motion WEC. For this purpose, a new design methodology is proposed in this paper for identifying and assessing possible floating configurations of CECO, which consists of four distinct set-ups obtained by varying the type of main supporting structure and the mooring system. Two options are based on spar designs and the other two on tension leg platform (TLP) designs. Based on outcomes of time-domain numerical calculations, the aforementioned configurations were assessed in terms of annual wave energy conversion and magnitude of mooring loads. Results indicate that a TLP configuration with an innovative mooring solution could increase the annual energy production by 40% with respect to the fixed version of CECO. Besides, the mooring system is found to be a key component, influencing the overall system performance.