  In a model independent manner, we explore the local implications of a single
neutrino oscillation measurement which cannot be reconciled within a
three-neutrino theory. We examine this inconsistency for a single region of
baseline to neutrino energy $L/E$. Assuming that sterile neutrinos account for
the anomaly, we find that the {\it local} demands of this datum can require the
addition to the theory of one to three sterile neutrinos. We examine the
constraints which can be used to determine when more than one neutrino would be
required. The results apply only to a given region of $L/E$. The question of
the adequacy of the sterile neutrinos to satisfy a global analysis is not
addressed here. Finally, using the results of a 3+2 analysis, we indicate
values for unknown mixing matrix elements which would require two sterile
neutrinos due to local demands only.
