Sample sizes for multilevel modeling

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Dimensions of Socio-economic Status and their Relationship to Mathematics and Science Achievement at Individual and Collective Levels (2003, background): “It may be due to the fact that countries have different group-level sample size and intraclass correlations among the SES indicators (Hox & Maas, 2002).”
Examining the Rule of Thumb of Not Using Multilevel Modeling: The “Design Effect Smaller Than Two” Rule (2015, background): “Sometimes they apply the rule of thumb that “[i]f the design effect is smaller than two, using single level analysis on multilevel data does not seem to lead to overly misleading results” (Hox & Maas, 2002, p. 5; see also B. O. Muthén & Satorra, 1995).”
EDA for HLM: Visualization when Probabilistic Inference Fails (2005, methodology): “They advise at least 50 groups in order to have correct coverage of confidence intervals on all pieces of the multilevel model (the fixed coefficients and the variance components) (Maas and Hox, 2002; Hox and Maas, 2002; Maas and Hox, 2004).”