A central composite design (CCD) study was conducted to understand the relationship among dietary branched-chain amino acids (BCAA) on live performance, carcass traits, and feather composition in Ross 344 × 708 male broilers. A total of 2,592 d-old male chicks were randomly placed into 144-floor pens. Each pen received 1 of 16 dietary treatments from 20 to 35 d of age varying in digestible ratios of Ile:Lys (52 to 75), Val:Lys (64 to 87), and Leu:Lys (110 to 185) arranged as CCD. Birds and feed were weighed at 20 and 34 d of age to determine body weight gain (BWG), feed intake, and feed conversion ratio (FCR). At 35 d of age, all birds except 1 were processed to determine carcass characteristics. Feather dry matter, protein, and amino acid compositions were determined from the last 5 primary feathers of 1 bird per pen. Data were analyzed as CCD using the surface response option of JMP v.15. Body weight gain (1,332 g; P < 0.001; R2 = 0.93) and FCR (1.54; P = 0.002; R2 = 0.88) from 20 to 34 d of age were optimized at the lowest Leu:Lys ratio (110) with minimum Val:Lys (78 to 79) and Ile:Lys (65 to 66) ratios. Poorer BWG and FCR were observed as Leu:Lys ratio increases although increasing Val:Lys and Ile:Lys ratios alleviated the poor performance. Opposite to live performance, both carcass (71.5%; P = 0.031; R2 = 0.76) and breast yield (26.7%; P < 0.001; R2 = 0.96) were maximized at the highest Leu:Lys ratio. This effect was complemented by increasing Ile:Lys ratio beyond 68. In contrast, it requires lower Ile:Lys and Val:Lys ratios to maximize carcass and breast yield at the lowest Leu:Lys ratio but with lower meat yields than in high Leu:Lys ratio. Feather protein content was the highest (96.1%) when increasing Ile:Lys ratio to 70 (P = 0.07) with Leu:Lys and Val:Lys ratios of 110 and 80, respectively. Increasing Leu:Lys ratio to 185 decreased maximum feather protein content to 93.5%.