We investigate the spontaneous breaking of subsystem symmetry in a stack of two-dimensional Fermi liquid metals, each maintaining a subsystem number conservation symmetry, driven by interlayer exciton condensation. The resulting Goldstone modes in this broken symmetry phase couple to the quasiparticle current perpendicular to the layers. This coupling, which remains nonzero for small momentum transfers, leads to the emergence of a three-dimensional anisotropic marginal Fermi liquid state when the number of layers is sufficiently large. We propose a possible experimental realization of this phenomenon in two-dimensional multilayer van der Waals heterostructures. Using self-consistent mean-field calculations, we characterize the subsystem symmetry-broken metallic state and examine the effects of fluctuations on its physical properties within the random phase approximation. We find that these fluctuations produce additional logarithmic enhancements to the specific heat at low temperature, specifically $C\sim T[\log (1/T){]}^2$.

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• Excitons
• Exotic phases of matter
• Specific heat
• Layered crystals
• Non-Fermi-liquid theory