  We develop a reduction scheme for the $L_\infty$-algebra of observables on a
premultisymplectic manifold $(M,\omega)$ in the presence of a compatible Lie
algebra action $\mathfrak{g}\curvearrowright M$ and subset $N\subset M$. This
reproduces in the symplectic setting the Poisson algebra of observables on the
Marsden-Weinstein-Meyer symplectic reduced space, whenever the reduced space
exists, but is otherwise distinct from the Dirac, \'Sniatycki-Weinstein, and
Arms-Cushman-Gotay observable reduction schemes. We examine various examples,
including multicotangent bundles and multiphase spaces, and we conclude with a
discussion of applications to classical field theories and quantization.
