Refractory multi-principal element alloys (RMPEAs) have gained interest recently due to their superior properties at elevated temperatures, including outstanding yield and ultimate strengths, high thermal conductivity, and resistance to creep. RMPEAs can be designed to exhibit a wide range of properties by tailoring their composition. However, the vast chemical design space makes brute-force experimental screening inefficient and costly. In this work, we follow a closed-loop, iterative computational/experimental screening approach that combines computational alloy design methodologies with high-throughput synthesis and characterization tools to explore the vast RMPEAs space and design new RMPEAs that satisfy multiple objectives and constraints. In particular, we targeted compositions with yield strengths higher than 50 MPa at 2000 °C, W content of more than 30 at.% for high-temperature strength and operability up to 2000 °C, narrow solidification range for additive manufacturability, competitive ductility metrics, among other property constraints. We evaluated the mechanical properties and microstructure of 58 alloys designed in 5 batches, in both as-cast and homogenized conditions, synthesized using vacuum arc melting, utilizing scanning electron microscopy, X-ray diffraction, Vickers microhardness, nanoindentation, and high-temperature compression testing. Based on the microhardness screening experiments in each batch, the best-performing alloys were selected for scale-up. High-temperature compression at 1800 °C was performed in these alloys, demonstrating that the designed alloys exhibit up to five times higher yield strength than a pure tungsten benchmark. We conclude that W-containing RMPEAs designed in this study merit further consideration for next-generation structural materials for ultra-high temperature applications.