We holomorphically embed nonlinear sigma models (NLSMs) on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ in the hyper-K{a}hler (HK) NLSM on the cotangent bundle of the Grassmann manifold $T^ast G_{2N,N}$, which is defined by $G_{N+M,M}=frac{SU(N+M)}{SU(N)times SU(M)times U(1)}$, in the ${mathcal{N}}=1$ superspace formalism and construct three-pronged junctions of the mass-deformed NLSMs (mNLSMs) in the moduli matrix formalism (MMF) by using a recently proposed method.