The current study aimed to compare the effects of increasing concentrations of dietary threonine (Thr), tryptophan (Trp), and glycine (Gly) on growth performance, stress biomarkers, and intestinal function in broiler chickens under multiple stress conditions. Five hundred sixty broiler chickens at 21 d old were randomly allotted to 5 treatments with 8 replicates. Birds in a positive control (PC) treatment were raised under low stock density (16.9 birds/m2 per cage) with recommended environmental conditions, whereas birds in 4 treatments were subjected to multiple stress conditions: a cyclic heat stress of 30 ± 0.3 °C for 10 h and 23 ± 0.2 °C for 14 h per day with high stock density (25.3 birds/m2 per cage). A basal diet was assigned to both PC and negative control (NC) treatments. Three additional diets were individually formulated to contain double concentrations of digestible Thr, Trp, or Gly + Ser compared with their concentrations in the basal diet. The experiment lasted for 14 d. Results showed that NC treatment had less growth performance (P < 0.001), jejunal goblet cell counts (P = 0.018), and trans-epithelial electrical resistance (TEER; P < 0.001), but greater (P = 0.026) feather corticosterone (CORT) concentrations than PC treatment. Thr treatment showed the least (P < 0.001) feed conversion ratio (FCR) among treatments under multiple stress conditions. Thr, Trp, and Gly treatments had less (P = 0.026) feather CORT concentrations, but had greater (P < 0.001) TEER than NC treatment. In conclusion, increasing concentrations of dietary Thr, Trp, or Gly improve the growth performance and intestinal health in broiler chickens with decreasing stress response under multiple stress conditions.