  The Casimir energy for $N$ $\delta$-function plates depends on multiple
scattering parameter $\Delta$. This $N$ body interaction was distributed into
two body interactions with nearest neighbour scattering and next-to-nearest
neighbour scattering based on partitions of $N-1$ and its permutations.
Implementing this methodology, we investigate Casimir energy for multiple
plates with constant conductivity relatable to Graphene. We also study Casimir
interaction between a perfect magnetic conductor and multiple constant
conductivity $\delta$ plates, which results in Boyer repulsion. In the
asymptotic limit for ideal boundary conditions, the results become simple where
multiple scattering parameter $\Delta$ consists only of nearest neighbour
scattering term.
