The anomalous Hall effect (AHE) and anomalous Nernst effect (ANE), which describe transverse electrical and thermoelectric responses in magnetic materials, respectively, are promising for spintronic and energy-harvesting applications. Here, we employ high-throughput first-principles calculations to investigate 2251 chemically substituted tetragonal L1₀ alloys. Among ferromagnets, enhanced responses emerge preferentially in alloys derived from parent compounds with small exchange splitting: no alloy derived from FePt, the archetypal L1₀ ferromagnet, reaches the high-response regime, whereas NiPt- and CoIr-derived alloys occupy it in large numbers. Small exchange splitting keeps majority- and minority-spin bands near the Fermi level, giving chemical substitution more opportunity to modify near-Fermi-level band crossings and amplify the Berry curvature. We predict a giant anomalous Hall conductivity of 2809 S cm⁻¹ in (Co_(0.8)Fe_(0.2))(Ir_(0.7)Pt_(0.3)) and a giant anomalous Nernst conductivity of 7.72 A m⁻¹ K⁻¹ in (Ni_(0.8)Co_(0.2))(Pt_(0.7)Ir_(0.3)). Our results identify the exchange splitting of the parent compound as a descriptor for chemical tunability toward giant Berry-curvature-driven transport responses.