Noncentrosymmetric superconductors (NCSs) are promising candidates for investigating spontaneous time-reversal symmetry breaking and topological superconductivity. This study aims to present a computational materials discovery and design process for developing CaPtAs-like NCSs. Through a comprehensive screening based on first-principles calculations, the range of CaPtAs-like materials is expanded to 13 compounds with superior stabilities, thereby indicating a high likelihood of synthesis. Based on the symmetry indicators diagnosis, SrPtAs, NaPtSi, and SrPtP were screened out as good candidates for investigating nodal superconductivity. Moreover, KPtP, CaRhAs, and CaPtSi were proposed as possible topological superconductor candidates. This investigation serves to aid in the design and expansion of the viable phase space for CaPtAs-like NCSs, and this screening framework may be extended to other NCS systems.