Layered two-dimensional (2D) materials have attracted considerable interest for their exotic and anisotropic electronic behavior. One such material, Sn₄As₃, bears a resemblance in both structure and elemental composition to two other Sn- and As-containing layered materials that have recently demonstrated axis-dependent conduction polarity: NaSn₂As₂ and NaSnAs. Here, a new family of Pb-alloyed Pb_xSn_4−xAs₃ crystals was synthesized and the axis-dependent electronic and thermoelectric properties were evaluated. Up to one full equivalent of Pb could be alloyed into Pb_xSn_4−xAs₃ (0 < x < 1.06) before phase separation occurred. We establish the structural changes and the trends in the Raman spectra with increasing Pb substitution. These materials all exhibit metallic temperature-dependent resistivities and positive thermopowers along the in-plane and cross-plane directions. The absence of axis-dependent conduction polarity in these SnAs-layered materials is consistent with theoretical predictions, and illustrates that precise control over the atomic and electronic structure and doping is essential for realizing this phenomenon in new materials.