The possible role of the social rank (R) (i.e., low-LSR, middle-MSR, or high-HSR) in anestrus goats exposed to a P4 + eCG (D) (i.e., 100 or 350 IU) estrus induction protocol (EIP) was evaluated. Goats (Alpine-Saanen-Nubian × Criollo; n = 70; 25° North) managed under stall-fed conditions were all ultrasound evaluated to confirm anestrous status, while the social rank was determined 30 d prior to the EIP. The response variables included estrus induction (EI, %), duration of estrus (DUR, h), ovulation rate (OR, n), live weight (LW, kg), thoracic perimeter (TP, cm), thoracic diameter (TD, cm), body length (BL, cm), height at withers (HW, cm), beard length (BEA, cm), compactness index (COM, cm), and anamorphosis index (ANA, cm), as affected by R, D, and the R × D interaction were evaluated, while the correlation coefficients among reproductive and morphometric variables were quantified. An R × D interaction (p < 0.05) affected the response variables EI, DUR, and OR. While the largest (p < 0.05) EI% occurred in the HSR goats, irrespective of eCG (i.e., 100 or 350 IU), both the shortest estrus duration (DUR, h) and the lowest ovulation rate (OR, n) occurred in the LSR + D100 combination, with no differences among HSR and MSR either with D100 or D350. Regarding the LW and morphometric response variables, (i.e., LW, TP, TD, BL, HW, BEA, COM, and ANA) all of them favored either the HSR and MSR groups, with the lowest phenotypic values occurring in the LSR-goats. The EI% was observed to be positively correlated (p < 0.05) with DUR (0.71), LW (0.28), TP (0.31), TD (0.34), BL (0.33), HW (0.35), COM (0.23), and ANA (0.23). While DUR was correlated (p < 0.05) with TP (0.26) and ANA (0.24), OR demonstrated no-correlation (p > 0.05) with any response variable, either reproductive or morphometric. As expected, LW had high correlation coefficients (p < 0.01) with TP (0.86), TD (0.88), BL (0.82), HW (0.75), BEA (0.51), COM (0.97), and ANA (0.75). In general, the morphometric variables as a whole demonstrated important correlation coefficients among them (p < 0.01), ranging from 0.38 up to 0.84. To estimate the importance of the morphometric differences between social rank upon estrus induction, a principal component (PC) analysis was performed based on the correlation matrix derived from the corporal measurements. The PC1 and PC2 explained 70.3% and 17.6% of the morphometric variation, respectively. The PC1 was a measure of the goat size (i.e., small, medium, large) and its association with estrus occurrence was evaluated using a logistic regression model; the bigger the goat, the increased probability of being in estrus, by up to five times compared to small goats. Our results confirm that the higher social ranked, larger goats amalgamated some fundamental factors to be successful: aggressiveness, primacy to food access, augmented live weight, and corporal size; all of these were able to modulate out-of-season reproductive success in crossbred dairy goats subjected to an estrus induction protocol and managed under stall-fed conditions in Northern Mexico.