Let Y be a smooth algebraic stack exhausted by quotient stacks. Given a Kirwan-Ness stratification of the cotangent stack T^*Y, we establish a recollement package for twisted D-modules on Y, gluing the category from subquotients described via modules microsupported on the Kirwan-Ness strata of T^*Y. The package includes unusual existence and "preservation-of-finiteness" properties for functors of the full category of twisted D-modules, extending the standard functorialities for holonomic modu...