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Introduction/Background. SNAP has persistent non-take-up: one in six likely-eligible households does not participate. Prior research documents take-up gaps by race, rurality, and family structure as separate axes; whether these dimensions compound into distinctively intersectional barriers has not been quantified nationally. We use multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA) to decompose intersectional variance and identify strata where additive expectations fail.Purpose/Research Question. Among likely-eligible adult women, we ask: (1) how much take-up variance lies between intersectional strata; (2) how much is explained by additive main effects of race/ethnicity, rurality, and household structure; and (3) which strata show residuals excluding zero after adjustment. Pre-specified Hypothesis 5 anticipated negative residuals among multiply-marginalized strata (minority × nonmetro × with-children).Data. Data were drawn from the 2015–2019 American Community Survey Public Use Microdata Sample. Likely-eligible women aged 18+ were identified using state-specific Broad-Based Categorical Eligibility thresholds (most commonly ≤200% of the federal poverty line); one woman per household was retained by random selection (N = 1,207,252; SNAP receipt = 33.0%). Intersectional strata crossed six race/ethnicity categories (one aggregating Native Hawaiian or Pacific Islander, Some Other Race, and Two-or-More-Races) with three rurality and four household-structure categories, yielding 72 strata across 51 states.Research Design and Methods. We estimated cross-classified logistic MAIHDA models by Bayesian MCMC in R2MLwiN (MLwiN default priors, Gamma [0.001, 0.001] on precisions; four chains × 200,000 iterations after 50,000 burn-in), with a frequentist cross-check in lme4 (glmer). Three models were fit: a null model (M₀); an additive main-effects model with year fixed effects (M₁); and M₁ₐ, a year-free refit decomposing the M₀→M₁ variance reduction. Estimands: between-stratum variance partition coefficient (VPC), proportional change in variance (PCV), median odds ratio (MOR), and stratum-level posterior medians with 95% credible intervals (CrIs). All models converged (R̂ ≤ 1.01; M₀ minimum ESS = 1,195).Results/Findings. The null-model VPC was 13.08% (95% CrI [9.99, 17.20]), ≈2.4× the MAIHDA-corpus median; null-model MOR was 1.95 (95% CrI [1.80, 2.23]). Additive main effects accounted for 95.6% of between-stratum variance; residual VPC ≈ 0.64%. Year fixed effects added no signal (σ²ᵤ in M₁ and M₁ₐ ≈ 0.021). Bayesian and frequentist VPCs concurred (13.08% vs. 12.97%). Four of 72 strata had posterior residuals with CrIs excluding zero: three positive (non-Hispanic White nonmetro single-with-children, +0.22; non-Hispanic AIAN nonmetro partnered-with-children, +0.20; non-Hispanic Black nonmetro single-with-children, +0.16) and one negative (non-Hispanic Black large-metro partnered-with-children, −0.14). Contrary to Hypothesis 5, residuals did not concentrate as predicted; the positive cluster in nonmetro strata with children may reflect community-based enrollment, peer referrals, or FDPIR (Food Distribution Program on Indian Reservations) substitution among AIAN households rather than deficit mechanisms.Conclusion/Implications. Intersectional position meaningfully structures SNAP take-up (VPC ≈ 13%), yet the patterning is predominantly additive. This aligns with administrative-burden theory: uniform state policy rules impose racialized costs that accumulate across dimensions rather than compound at specific intersections. Reform targeting marginal disadvantages, rather than fully crossed intersectional design, addresses the dominant patterning. The residual marks where single-axis approaches underperform; mechanisms remain ambiguous between administrative burden and household agency.