We present the first three-parameter fit to a 3+1 sterile neutrino model using 7.634 years of data from the IceCube Neutrino Observatory on νμ+ν‾μ charged-current interactions in the energy range 500–9976 GeV. Our analysis is sensitive to the mass-squared splitting between the heaviest and lightest mass state (Δm412), the mixing matrix element connecting muon flavor to the fourth mass state (|Uμ4|2), and the element connecting tau flavor to the fourth mass state (|Uτ4|2). Predicted propagation effects in matter enhance the signature through a resonance as atmospheric neutrinos from the Northern Hemisphere traverse the Earth to the IceCube detector at the South Pole. The remaining sterile neutrino matrix elements are left fixed, with |Ue4|2=0 and δ14=0, as they have a negligible effect, and δ24=π is set to give the most conservative limits. The result is consistent with the no-sterile neutrino hypothesis with a probability of 4.3%. Profiling the likelihood of each parameter yields the 90% confidence levels: 2.4eV2<Δm412<9.6eV2, 0.0081<|Uμ4|2<0.10, and |Uτ4|2<0.035, which narrows the allowed parameter-space for |Uτ4|2. However, the primary result of this analysis is the first map of the 3+1 parameter space exploring the interdependence of Δm412, |Uμ4|2, and |Uτ4|2.