  We present a comprehensive analysis of the vacuum stability of the Two-Higgs
Doublet Model, for both Type-I and Type-II, augmented by vector-like quarks in
either singlet, doublet or triplet representations. We review the model briefly
before introducing the extra fermionic states and their interactions, and
impose restrictions on the parameters coming both from theoretical
considerations and experimental bounds. We then study the renormalization group
equation evolution of the parameters of the model in order to isolate the
parameter regions that satisfy vacuum stability requirements. We then add the
electroweak precision observables to insure that the resulting parameter space
is consistent with the data. We include complete expressions for the
renormalization group equations and the S and T parameters used. Finally we
summarize the effects of various vector-like quark representations on the
parameter space. We indicate the regions constrained, highlighting the
differences between representations in Type-I and Type-II, and pinpoint the
effects of the interplay between the extended model and the additional
fermions.
