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Interpreting the small-scale clustering of galaxies with halo models canelucidate the connection between galaxies and dark matter halos. Unfortunately,the modelling is typically not sufficiently accurate for ruling out modelsstatistically. It is thus difficult to use the information encoded in smallscales to test cosmological models or probe subtle features of the galaxy-haloconnection. In this paper, we attempt to push halo modelling into the"accurate" regime with a fully numerical mock-based methodology and carefultreatment of statistical and systematic errors. With our forward-modellingapproach, we can incorporate clustering statistics beyond the traditionaltwo-point statistics. We use this modelling methodology to test the standard$\Lambda\mathrm{CDM}$ + halo model against the clustering of SDSS DR7 galaxies.Specifically, we use the projected correlation function, group multiplicityfunction and galaxy number density as constraints. We find that while the modelfits each statistic separately, it struggles to fit them simultaneously. Addinggroup statistics leads to a more stringent test of the model and significantlytighter constraints on model parameters. We explore the impact of varying theadopted halo definition and cosmological model and find that changing thecosmology makes a significant difference. The most successful model we tried(Planck cosmology with Mvir halos) matches the clustering of low luminositygalaxies, but exhibits a 2.3$\sigma$ tension with the clustering of luminousgalaxies, thus providing evidence that the "standard" halo model needs to beextended. This work opens the door to adding interesting freedom to the halomodel and including additional clustering statistics as constraints.

Towards Accurate Modelling of Galaxy Clustering on Small Scales: Testing the Standard $\Lambda\mathrm{CDM}$ + Halo Model