The critical current of multifilamentary Nb-Hf/Cu-Sn-Ga has been determined as a function of both field and strain at fields from 4 to 19 T. The strain dependence of the critical current is significantly reduced compared with that of commercial multifilamentary Nb3Sn superconductors. This reduced strain sensitivity, coupled with an enhanced critical-current density above 12 T, make this a candidate material for economic high-field magnet construction. An analysis of the data in terms of the strain scaling law indicates that the Hf and Ga additives do not produce this improvement through a decrease in the strain sensitivity of the bulk upper critical field B*c2. Rather, they reduce the strain sensitivity of the critical current through a changed shape of the flux pinning curve and an enhancement in the strain-free maximum value of B*c2 (B*c2m = 25 T for Nb-Hf/Cu-Sn-Ga versus 21 T for Nb3Sn).