We present a comprehensive analysis of the vacuum stability of the two-Higgs-doublet model, for both type-I and type-II, augmented by vectorlike quarks in 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 from both 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 ensure 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 vectorlike 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.