A family of decompositions {G₀,G₁,...,G_{r-1}} of a complete bipartite graph K_{n,n} is a set of r mutually orthogonal graph squares (MOGS) if G_{i} and G_{j} are orthogonal for all i,j∈{0,1,...,r-1} and i≠j. For any subgraph G of K_{n,n} with n edges, N(n,G) denotes the maximum number r in a largest possible set {G₀,G₁,...,G_{r-1}} of MOGS of K_{n,n} by G. In this paper we compute two extensions of the well-known N(n,G)=r≥4, where n=11, G=(4K_{1,2}∪3K₂), and n=13, G=(3K_{1,2}∪7K₂). A family of decompositions {G₀,G₁,...,G_{r-1}} of a complete bipartite graph K_{n,n} is a set of r mutually orthogonal graph squares (MOGS) if G_{i} and G_{j} are orthogonal for all i,j∈{0,1,...,r-1} and i≠j. For any subgraph G of K_{n,n} with n edges, N(n,G) denotes the maximum number r in a largest possible set {G₀,G₁,...,G_{r-1}} of MOGS of K_{n,n} by G. In this paper we compute two extensions of the well-known N(n,G)=r≥4, where n=11, G=(4K_{1,2}∪3K₂), and n=13, G=(3K_{1,2}∪7K₂).