Reliable mechanical characterization of spinal cord tissue is essential for understanding the mechanisms of spinal cord injury (SCI). However, the tissue's ultrasoft nature and the complex ``butterfly'' arrangement of gray matter (GM) within white matter (WM) make full characterization difficult. Traditional methods typically rely on indentation for local properties, which lacks large-strain data or tension response information. Meanwhile, the individual gray and white matter regions are too small in size to extract and conduct independent macroscale tension-compression tests. To address this, we introduce a multi-modal approach, which combines mesoscale indentation of GM and WM with macroscale cyclic compression-tension tests. This multi-modal approach introduces a modeling challenge: ensuring that parameters derived across scales are directly comparable. While a one-term Ogden model captures indentation behavior, a two-term Ogden model (defined by µ1, ⍺1 and µ2, ⍺2) is generally required for nonlinear tension-compression stiffening. In standard formulations, these parameters are inherently coupled, meaning each influences both loading regimes simultaneously. To decouple these effects, we developed a modified two-term Ogden model, introducing a scaling parameter, n, such that µ2 = n µ1, where sensitivity analysis identifies the value of n such that nonlinear stiffening responses are effectively isolated. Shear moduli identified from both mesoscale and macroscale tests were found to be consistent; whole-sample rheometer values (66 ± 22 Pa) fell within the range of individual GM and WM results (66 ± 44 to 68 ± 39 Pa, for comparable loading rate) . This work establishes a robust framework for identifying scale- and loading-mode-dependent material parameters, providing the high-fidelity mechanical data necessary for realistic computational models of the central nervous system.