The resurgence in the literature on the reduced dependence of elastic constants for damaged materials and composites has been largely inspired by the exploration of the stress invariance under a modulus shift by Cherkeav and others in 1992 (henceforth referred to as the CLM shift) in planar elasticity. However, a CLM shift can at most reduce the dependence of two elastic constants. The present work devises an approach that combines the CLM shift and an orthotropic transform. As a result, the governing equation of a general planar anisotropic solid only contains a single dimensionless elastic constant (denoted by |c∗2| in this paper) in the transformed coordinates. The damage compliance of a solid with holes can be expressed explicitly through a function depending only on |c∗2|. If an elastic composite consists of a matrix and inclusions of aligned anisotropy, its overall compliance can be expressed through a function of three combinative parameters, namely |c∗2| and two Dundurs parameters. Furthermore, a configuration invariant transform is found for layered materials of aligned anisotropy. The stress analysis of such configurations only involves four elastic constants.