We study the thermal static potential for (2+1)-flavor QCD at nonzero density through a Taylor expansion around vanishing chemical potentials. From Taylor expanded Wilson line correlators, we extract the $\hmu^2$ coefficient of the real and imaginary part of the potential in light and strange flavor channels and in the baryon number and electric charge channels. We observe an enhancement of in-medium screening at intermediate and large separations. The effect is visible in both the real and imaginary parts to the extracted $\hmu^2$ contribution of the static potentials and provides a first step toward constraining in-medium heavy-quark interactions relevant for the Beam Energy Scan program at RHIC and future FAIR experiments.