Is it possible in AMReX to refine “half” a coarse cell (i.e., partial refinement) so that fine-cells are fully enclosed by adjacent coarse nodes?

[Afraid31]

I have a question about how AMReX handles refinement between levels in 2D, specifically for cell-centered data.

In the standard case with refinement ratio 𝑟=2, each coarse cell is divided into 2×2 fine cells, so the coarse-cell center is surrounded by four fine-cell centers.

I’m exploring an alternative geometric viewpoint where the four coarse-cell corners (nodes) act as the border enclosing the four fine cells — as sketched in Grid diagram A.

Grid diadiagram A
My question

Is it possible, within AMReX’s AmrLevel framework, to refine only part of a coarse cell (e.g., half of it) while leaving the other half coarse, so that the fine cells remain enclosed by surrounding coarse nodes?
In other words, can AMReX support this kind of partial-coarse-cell refinement — refining part of a coarse cell but not the whole — while maintaining proper cell-to-cell mapping, overlap, and flux conservation?