A \((G, \overline{G})\) -multidesign of \(K_n\) is the multidecomposition of the complete graph \(K_n\) into copies of the graph G and its complement \(\overline{G}\) . In this paper, we introduce and discuss the concepts of complementing multidesign, subdesign, and uniform k-multidesign of complete graphs. We study the importance of \((C_4 \cup P_2, \overline{C_4 \cup P_2})\) in the multidesign of \(K_n\) , where \(\overline{C_4 \cup P_2}\) denotes the two point union of two \(K_4-e\) graphs and \(C_4 \cup P_2\) denotes its complement. We also discuss the above properties for this graph pair. The structures like subdesigns, complementing multidesigns, and other multidesigns can help to improve Shamir’s Secret sharing scheme, which presents a technique for allocating a secret among participants so that it can only be recreated if an adequate number of participants combine their information.