find new materials (i) with low effective masses, required to achieve high μ, and (ii) with low defect densities and/or capture cross sections, required to achieve high τ. While we do not have exact answers to these questions at this stage, we will argue in the next three sections that there is significant scope for the discovery of new PSs with such desirable properties. The three main strategies we will outline are: Increasing the number of elements from ternary to quaternary compounds (Sec. 4.1), exploring P-rich compositions with P/S ≥ 1 (Sec. 4.2), and exploiting the chemical versatility of phosphorus (Sec. 4.3).