We construct a composite two-Higgs-doublet model (2HDM) within the context of dilaton effective field theory. This EFT describes the particle spectrum observed in lattice simulations of a near-conformal SU (3) gauge field theory. A second Higgs doublet is naturally accommodated within the EFT, used previously to construct a one-Higgs-doublet model. We explore the interplay of phenomenological and EFT requirements, supplemented by information from numerical lattice studies of the SU (3) gauge theory with eight fundamental (Dirac) fermions. We build a viable model with moderate parameter tuning. In the relevant portion of parameter space, we match the model to a conventional general description of 2HDMs, and comment on the role of custodial symmetry (breaking) in the scalar potential. Contributions to the precision electroweak parameter T provide a possible explanation for the recent measurement of the W-boson mass by CDF II.1 We adopt Mπ = 4 TeV as an indicative reference mass scale for the PNGBs. This scale could be lowered, and the fine tuning further softened, as some experimental bounds from direct searches involve suppressed model-dependent couplings that enter certain production rates. See for instance Refs. [71,72] for useful dedicated phenomenological studies.