Two-color high-harmonic spectroscopy is widely used to access sub-cycle electron dynamics and to retrieve harmonic timing information, including harmonic phases and attochirp across gases, solids, and liquids. However, the dependence of such timing observables on additional laser-control parameters remains largely unexplored. Here, we introduce driving intensity as an additional dimension of two-color harmonic spectroscopy in highly oriented pyrolytic graphite (HOPG). The retrieved attosecond two-color delays maximizing the 4th and 5th harmonic yields evolve systematically and differently with driving intensity. Semiconductor Bloch-equation calculations reproduce these trends and reveal a pronounced sensitivity of the intensity-dependent delays to the electronic band dispersion. Our results demonstrate multidimensional attosecond clocking near Dirac cones and establish intensity-dependent two-color delays as a sensitive observable for band-dispersion in quantum materials.