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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 nu(mu) + (nu) over bar (mu) 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 (Delta m(41)(2)), the mixing matrix element connecting muon flavor to the fourth mass state (vertical bar U-mu 4 vertical bar(2)), and the element connecting tau flavor to the fourth mass state (vertical bar U-tau 4 vertical bar(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 vertical bar U-e4 vertical bar(2) = 0 and delta(14) = 0, as they have a negligible effect, and delta(24) = pi 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: 2.4 eV(2) < Delta m(41)(2) < 9.6 eV(2), 0.0081 < vertical bar U-mu 4 vertical bar(2) < 0.10, and vertical bar U-tau 4 vertical bar(2) < 0.035, which narrows the allowed parameter-space for vertical bar U-tau 4 vertical bar(2). However, the primary result of this analysis is the first map of the 3+1 parameter space exploring the interdependence of Delta m(41)(2), vertical bar U-mu 4 vertical bar(2), and |U-tau 4 vertical bar(2).