A total of 48 high genetic merit (HM) and 48 medium merit (MM) cows, each given a low (LC), medium (MC), or high (HC) level of concentrate supplementation, were used in a split-plot design experiment, which was run in three consecutive years, to evaluate animal production responses. Individual cow intakes were estimated twice each year while at pasture; measurement period 1 (MP1) was in May/June, and measurement period 2 (MP2) was in early September, corresponding on average to d 110 and 200 of lactation, respectively. In MP1, cows were offered 0 (LC), 3 (MC), and 6 kg (HC), whereas in MP2 the levels were 0 (LC), 0 (MC), and 4 kg (HC) of concentrate daily. Genotype had a significant effect on all milk production parameters in MP1 and MP2. The HM cows had the highest yield of milk, fat, protein, and lactose, whereas the MM cows had the highest milk fat, protein, and lactose concentrations. The HM cows had significantly higher grass dry matter intake (GDMI) estimates. In MP1, the average responses, per kg concentrate dry matter, was +1.10 kg of milk, +0.038 kg of protein, +0.032 kg of fat. The corresponding values in MP2 were +0.94 kg of milk, +0.037 kg of protein, and +0.025 kg of fat. The response to concentrate was linear and independent of preexperimental milk yield. In MP1, the partial regression coefficients relating daily GDMI to an increase in 1 kg of preexperimental milk yield (PMY), preexperimental BW (PBW), and concentrate intake (CI) were 0.123, 0.006, and -0.54, respectively, whereas the corresponding values in MP2 were 0.190,0.007, and-0.444, respectively. This study indicates that with high yielding dairy cows, on gras only GDMI of 17 kg of supporting milk yield of 30-kg/d is achievable. In this scenario, concentrate supplementation will result in lower substitution rates, and higher milk yield response than previously published with lower yielding cows.