We present a SUSY model with four Higgs doublets of the“private type,”in which all fermion types(up,down,and charged leptons)obtain their masses from a different Higgs doublet Hf(f = u1,d,e).The conditions for anomaly cancellation imply that the remaining Higgs doublet of the model(Hu2)must have the same hyper-charge as Hu1,and thus,can only couple to up-type quarks,which opens the possibility to have FCNCs only in this sector.We study the Lagrangian of the model,and in particular,the Higgs potential,to identify the Higgs mass-ei-genstates and their interactions;for the Yukawa matrices,we consider the four-texture case.We obtain constraints on the model parameters by using LHC measurements on the properties of the 125 GeV Higgs boson(h),and identi-fy viable regions of the parameter space.Subsequently,these constraints are used to evaluate the prospects for de-tecting the FCNC decay mode t→ch at the future high-luminosity(HL)option for the LHC,which are compared with current limits from LHC-run2.Moreover,we evaluate the FCNC decay of the next heavier Higgs boson H2→tc,which can typically reach BR(H2→tc)≈ 0(10-4-10-5).The search for the signal at HL-LHC is also studied,and it is found that it may be detectable for specific regions of the model parameter space.