Keeping a binary search tree by splitting nodes (like a B-Tree)
1-2 Brother Trees, as in "Purely Functional 1-2 Brother Trees" by Ralf Hinze in some way allow splitting a node. Like in 2-4 trees where nodes have 2 to 4 children, in 1-2 brother trees, nodes have 1 to 2 children.

The advantages are a bit hand-wavey: it is sometimes faster, and sometimes simpler, and sometimes uses less space.