Designer non-Abelian fractons from topological layers

We formulate a construction of type-I fracton models based on gauging planar subsystem symmetries of topologically ordered two-dimensional layers that have been stacked in three ambient spatial dimensions. Via our construction, any defect of an Abelian symmetry group in a two-dimensional symmetry-enriched topological order can be promoted to a fracton. This allows us to construct fracton models supporting chiral boundaries and fractons of noninteger quantum dimension. We also find a lineon model supporting non-Abelian surface fractons on its boundary.