We present an atlas and follow-up spectroscopic observations of 87 thin stream-like structures detected with the STREAMFINDER algorithm in Gaia DR3, of which 28 are new discoveries. Here, we focus on using these streams to refine mass models of the Galaxy. Fits with a double-power-law halo with the outer power-law slope set to ‑β h = ‑3 yield an inner power-law slope of $-{\gamma }_{h}=-({0.97}_{-0.21}^{+0.17}\,)$ , a scale radius of ${r}_{0,h}={14.7}_{-1.0}^{+4.7}\,\mathrm{kpc}$ , a halo density flattening q m,h = 0.75 ± 0.03, and a local dark matter density of ρ h,⊙ = 0.0114 ± 0.0007 M ⊙ pc‑3. Freeing β yields $\beta ={2.53}_{-0.16}^{+0.42}$ , but this value is heavily influenced by our chosen virial mass limit. The stellar disks are found to have a combined mass of ${4.20}_{-0.53}^{+0.44}\times {10}^{10}\,{M}_{\odot }$ , with the thick disk contributing 12.4% ± 0.7% to the local stellar surface density. The scale lengths of the thin and thick disks are ${2.17}_{-0.08}^{+0.18}$ and ${1.62}_{-0.13}^{+0.72}\,\mathrm{kpc}$ , respectively, while their scale heights are ${0.347}_{-0.010}^{+0.007}$ and ${0.86}_{-0.02}^{+0.03}\,\mathrm{kpc}$ , respectively. The virial mass of the favored model is ${M}_{200}={1.09}_{-0.14}^{+0.19}\times {10}^{12}\,{M}_{\odot }$ , while the mass inside of 50 kpc is M R<50 = 0.46 ± 0.03 × 1012 M ⊙. We introduce the Large Magellanic Cloud (LMC) into the derived potential models, and fit the Orphan stream therein, finding a mass for the LMC that is consistent with recent estimates. Some salient highlights include the nearby trailing arm of ω Cen, and a nearby very metal-poor stream that was once a satellite of the Sagittarius dwarf galaxy. Finally, we unambiguously detect a hot component around the GD-1 stream, consistent with it having been tidally preprocessed within its own dark matter subhalo.