In recent work, Y. Takeyama identified a deformation of affine Hecke algebra. The algebra is generated by the multiplication and difference operators, later discussed by Lascoux and Schutzenberger. This algebra has two representations, first on a Laurent polynomial ring and second on the vector space of C-valued functions on the orthogonal, $k$-dimensional lattice. Further, Takeyama constructed a Hamiltonian, $H$, that specifies an integrable stochastic one-dimensional particle system with continuous time for surface diffusion. This is due to a commutation relation, $HG=GL$, involving the Hamiltonian, $H$, a propagation operator, $G$, and a Laplacian operator, $L$, that allows finding the eigenvectors of $H$. We aim to consider an extended Laplacian, $L_{ext}$, to include not only $k$ but all $2k$ unit vectors the orthogonal, $k$-dimensional lattice. Then for the extended Laplacian, we aim to find the Hamiltonian, $H_{ext}$, that satisfies the commutation relation $H_{ext}G=GL_{ext}$. Consequently, the new Hamiltonian would result in another integrable stochastic particle system with dynamics that involves particle movement in both left and right directions.