  We introduce an $R$-matrix acting on the tensor product of MacMahon
representations of Ding-Iohara-Miki (DIM) algebra
$U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs
of $3d$ Young diagrams and retains the nice symmetry of the DIM algebra under
the permutation of three deformation parameters $q$, $t^{-1}$ and
$\frac{t}{q}$. We construct the intertwining operator for a tensor product of
the horizontal Fock representation and the vertical MacMahon representation and
show that the intertwiners are permuted using the MacMahon $R$-matrix.
