We have synthesized previously unreported high-entropy alloys (HEAs) in the pentanary (ScZrNb)1–x[RhPd]x and hexanary (ScZrNbTa)1–x[RhPd]x systems. The materials have CsCl-type structures and mixed site occupancies. Both HEAs are type-II superconductors with strongly varying critical temperatures (Tc’s) depending on the valence electron count (VEC); the Tc’s increase monotonically with decreasing VEC within each series, and do not follow the trends seen for either crystalline or amorphous transition metal superconductors. The (ScZrNb)0.65[RhPd]0.35 HEA with the highest Tc, ∼9.3 K, also exhibits the largest μ0Hc2(0) = 10.7 T. The pentanary and hexanary HEAs have higher superconducting transition temperatures than their simple binary intermetallic relatives with the CsCl-type structure and a surprisingly ductile mechanical behavior. The presence of niobium, even at the 20% level, has a positive impact on the Tc. Nevertheless, niobium-free (ScZr)0.50[RhPd]0.50, as mother-compound of both superconducting HEAs found here, is itself superconducting, proving that superconductivity is an intrinsic feature of the bulk material.