Nucleon decays into a lepton and two pseudoscalar mesons represent key channels for probing baryon number violation, complementing conventional two-body modes. In this Letter, we model-independently correlate two- and three-body processes within the framework of low-energy effective field theory, performing a global analysis that avoids single-operator-dominance assumption. We derive significantly improved bounds on 15 three-body modes with a lepton (e+, µ+, ν̂ = ν/ν̄) and two non-strange mesons (π, η). For charged-lepton modes, our indirect lower limits on partial lifetimes (Γ−1) are more stringent than current Particle Data Group (PDG) values by more than three orders of magnitude. For 5 (anti)neutrino modes, we establish for the first time Γ−1 ≳ 10^34 yr. Additionally, our analysis improves constraints on two-body processes n → e+π−, n → µ+π−, and p → ν̂π+ by approximately a factor of 2 compared to the PDG limits. These results highlight the importance of leveraging correlations among different processes to better probe new physics, enabling more stringent constraints on experimentally challenging processes from well-measured ones.