Schools of thought (madhabs)
Shafi'i inheritance
Egypt, the Levant, and Southeast Asia. Distinctive on the grandfather-with-siblings case and applies the Musharakah ruling.
The Shafi'i school dominates Egypt, the Levant, and Southeast Asia (Indonesia, Malaysia). Its inheritance rulings closely mirror Maliki and Hanbali, and stand against Hanafi on the contested special cases.
Distinctive Shafi'i positions
Applies Musharakah
Where Hanafi gives full siblings nothing in the Musharakah case, Shafi'i has them share with the maternal half-siblings in the 1/3 portion — even though they would otherwise be residuary heirs with no remainder to claim. The reasoning: they share the same mother, so it's just to include them.
Grandfather as a sibling on the case
On the grandfather-with-siblings case, Shafi'i computes three options for the grandfather (1/3 of remainder, share-as-sibling, 1/6 minimum) and gives him the largest. The same algorithm is used by Maliki and Hanbali, with minor sub-rule differences.
Applies Radd
Shafi'i has historically been more accepting of Radd than Maliki, and applies it readily in modern practice.