In this paper we examine the CDF Run II discovery reach for neutral
Higgs bosons via the process ppbar -> bb-bar phi -> bb-bar bb-bar.  The
signature is a four jet final state with at least three b-tagged jets.  Signal
and background acceptances are estimated using the CDF Run I detector
performance.  b tagging efficiencies and fake tag rates are evaluated with new
Run II increased detector geometrical acceptances.  Total rates are estimated
from present Run I data and from Monte Carlo.  The results are interpreted
within the framework of the minimal supersymmetric extension of the standard
model (MSSM) and generalized in terms of a model independence enhancement
factor.