Kronecker and plethysm coefficients are two fundamental families of nonnegative integers in combinatorial representation theory. Their study combines combinatorics, geometry, and representation theory, and understanding either family remains a major open problem in algebraic combinatorics. Both families arise in the representation theory of the Uniform Block Permutation (UBP) algebra. In this talk, I will show how computing restrictions and inductions of UBP representations can lead to combinatorial interpretations for certain special cases of plethysm coefficients. This is joint work with Saliola, Schilling, and Zabrocki