Superstring Field Theory with Double Background Independence

A recently constructed superstring field theory has two decoupled sectors, the physical superstring and a shadow sector with a second copy of the superstring. These are both expanded around the same background conformal field theory and the theory is independent of marginal deformations of this common background. A form of the action is presented that is symmetric between the two sectors. A generalisation of this theory is given in which the two sectors can be expanded around two different backgrounds, and the theory is independent under separate marginal deformations of the two background conformal field theories.