The paper presents analyses on stable prestressed configurations of the tensegrity triplex with non-minimal number of members. The non-minimal triplex is generally understood in the literature as the minimal triplex with three additional cables. However, this research shows that many different configurations can be obtained during prestressing. The prestressing procedure is lead by changing the lengths of selected groups of members, i.e. struts, base cables, cross cables or additional members, assuming symmetry. A different view on prestressing is presented, where typically understood tensegrity natural configuration is separated into a newly called geometrical configuration and natural lengths of attached members. The presented interpretation of prestressing has a clear physical meaning. The calculations are based on elastic energy approach, which is used to write the nonlinear equations that are afterwards solved numerically. Two examples of prestressing the non-minimal triplex are presented, for slender and stocky prisms dimensions. The results show that additional members usually understood in the literature as additional cables, can as well serve as struts, which leads to a new group of structures with tensegrity features.