Multisymplectic manifolds generalize symplectic manifolds by featuring a closed nondegenerate differential form of degree higher than 2. Such structures are natural candidates for a geometric formalization of classical field theories. In this context, Rogers (2010) showed that just as a symplectic manifold yields a Poisson algebra of functions, an n-plectic manifold yields an n-terms Lie infinity algebra of observables. The remarkable aspect of Rogers' construction is that it is essentially algebraic and relies only on the axioms of Cartan calculus, suggesting that this higher version of the "observable Poisson algebra" can be generalized beyond the realm of manifolds. In this talk, we propose such a generalization in the setting of Gerstenhaber algebras and Batalin–Vilkovisky (BV) modules, which provide an algebraic formulation of Cartan calculus of interests in the context of non-commutative geometry. This framework allows us to construct Lie infinity algebras of observables in a purely algebraic way, without reference to an underlying manifold. As an application, we turn to the problem of reducing multisymplectic observables in the presence of constraints or symmetries. Building on the work of Dippel, Esposito, and Waldmann, who introduced the notion of a "constraint triple" as a categorical package for coisotropic reduction, we adapt this formalism to our BV-module context and the associated Lie infinity algebras. This construction provides a conceptual framework for the algebraic reduction procedure of multisymplectic observables, as developed in our recent joint work with Casey Blacker (SIGMA 2024). The results presented here are part of a collaboration with Leonid Ryvkin, published in Differential Geometry and its Applications (2025).