Does Gini index considers only a binary split for each attribute or can it have multi way spliting?

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Does Gini-index based classification split values for any attribute always as a binary split or can it split into more than $2$ branches (multi-way split)?

For more clarification, if a split on $A$ partitions $D$ into $D_1$ and $D_2$ , the Gini-index of $D$ given that partitioning is,

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This is actually a binary split. Can there be also $D_4, D_5$ etc... too if it is not a binary split so that the formula will be,

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