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We present a forward-modeling framework to observationally infer the galaxy-halo connection in the dwarf galaxy regime. Our framework maps dark matter subhalo populations to four observable satellite properties —abundance, projected size, luminosity, and line-of-sight velocity dispersion — and statistically compares the resulting synthetic populations to observations. While previous analyses have typically relied on two or three observables, we jointly fit four, demonstrating that the dimensionality of the observable space matters as much as sample size.