Sparse ordinal response patterns can shift the sampling distributions of common confirmatory factor analysis (CFA) fit indices, making fixed heuristic cutoffs difficult to interpret across design conditions. We conducted a Monte Carlo simulation to calibrate scenario-specific cutoffs for the comparative fit index (CFI), TuckerâLewis index (TLI), root mean square error of approximation (RMSEA), and standardized root mean square residual (SRMR) in sparse five-category ordinal CFA and to evaluate their operating characteristics. Data were generated from a three-factor population model with one cross-loading. For each dataset, we fitted a Correct model, a Local Misfit model omitting the cross-loading, and a Severe Misfit model combining two factors. We varied estimator (robust maximum likelihood [MLR], mean- and variance-adjusted maximum likelihood [MLMV], weighted least squares mean- and variance-adjusted maximum likelihood [WLSMV]), sample size ( N = 250, 500, 1,000), loading strength ( $$\lambda$$ λ = .50 vs. .80), sparsity pattern, sparse-item scope, and category handling (original vs. collapsed). Cutoffs were calibrated from Correct-model distributions at $$\alpha$$ α = .05, using lower-tail quantiles for CFI and TLI and upper-tail quantiles for RMSEA and SRMR. Calibrated thresholds were strongly scenario-dependent. RMSEA and SRMR cutoffs were generally far below conventional benchmarks, whereas CFI and TLI cutoffs varied with sample size and loading strength, falling below .95 in lower-information settings and approaching boundary values in larger-sample and high-loading settings. Detection was substantially lower for Local Misfit than for Severe Misfit. A calibrated CFI-RMSEA AND rule provided a transparent multi-index operating profile, with false-rejection and detection trade-offs that varied across scenarios. Collapsing produced modest changes for robust ML estimators but increased WLSMV detection in lower-information settings. We provide cutoff tables, operating-characteristic summaries, an interpolation aid, and an applied illustration to support scenario-calibrated fit evaluation in sparse ordinal CFA.