Dark excitons play a central role in the nonequilibrium dynamics of two-dimensional semiconductors, but remain difficult to characterize. Transient-absorption experiments, with probes tuned in exciton-exciton transitions energy range (exc-tr-abs), can detect excitations from any populated dark excitons, including symmetry-forbidden, spin-forbidden, and finite-momentum ones. In this work, we develop a GW+BSE scheme for computing exc-tr-abs spectra from arbitrary populated exciton distributions. These dark excitons are included equally by evaluating exciton-exciton dipoles in a locally smooth gauge, including intra- and inter-band contributions. For monolayer MoS₂, the exc-tr-abs signal arises from the Γ, K, M, and Q valleys, differing substantially from the Γ-only interpretation. Exciton-exciton dipoles show similar intensities across these valleys, while their weights are dictated by initial excitonic populations. State- and spin-resolved analyses assign the peaks to 1s → 2p and 1s → 3p transitions from both spin-flip and spin-conserving A and B excitons across valleys and momenta.