Let P be a set of permutation patterns. If τ is a permutation that contains every element of P as a pattern, then we say that τ is a P -superpattern. Since Arratia coined the term in 1999, there have been several investigations into the length of the shortest Sk-superpattern, where Sk is the set of permutations of length k. Here, we will construct superpatterns for layered permutations of length k and explore an interesting connection between this set of superpatterns and plane binary trees on k vertices.