The work is concerned with the minimum residual norm subspace method based on the generalized conjugate residual method with inner orthogonalization that allows flexible preconditioning and deflated restarting for the solution of non-symmetric or non-Hermitian linear systems. The new inner-outer subspace method named FGCRO-DR is introduced. It is comparable expensive as existing FGMRES-DR (flexible generalized minimum residual with deflated restarting) in terms of computational operations per cycle, but FGCRO-DR offers the additional advantage to be suitable for the solution of sequences of slowly changing linear systems (where both the matrix and right-hand side can change) through subspace recycling. Numerical efficiency is shown on the example of multidimensional elliptic partial differential equations.