The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We investigate the ability of the short baseline neutrino (SBN) experimental program at Fermilab to test the globally-allowed (3 þ N) sterile neutrino oscillation parameter space. We explicitly consider the globally-allowed parameter space for the (3 þ 1), (3 þ 2), and (3 þ 3) sterile neutrino oscillation scenarios. We find that SBN can probe with 5σ sensitivity more than 85%, 95% and 55% of the parameter space currently allowed at 99% confidence level for the (3 þ 1), (3 þ 2) and (3 þ 3) scenarios, respectively, with the (3 þ N) allowed space used in these studies closely resembling that of previous studies [J. M. Conrad, C. M. Ignarra, G. Karagiorgi, M. H. Shaevitz, and J. Spitz, Adv. High Energy Phys. 2013, 1 (2013).], calculated using the same methodology. In the case of the (3 þ 2) and (3 þ 3) scenarios, CP-violating phases appear in the oscillation probability terms, leading to observable differences in the appearance probabilities of neutrinos and antineutrinos. We explore SBN's sensitivity to those phases for the (3 þ 2) scenario through the currently planned neutrino beam running, and investigate potential improvements through additional antineutrino beam running. We show that, if antineutrino exposure is considered, for maximal values of the (3 þ 2) CP-violating phase ϕ 54 , SBN could be the first experiment to directly observe ∼2σ hints of CP violation associated with an extended lepton sector.