Although the Chinese government has shifted from a one-child policy to a two-child policy (allowing a couple to have up to two children) since 2016 in response to the aging population, the policy results have been unsatisfactory. This is the first paper to systematically investigate the factors influencing residents’ intentions to have a second child. The research focuses on the perspective of individual, family, and social characteristics based on the Chinese General Social Survey (CGSS) from 2017 to 2018. Three machine learning methods are used in conjunction with logistic regression to reveal that the intention of having a second child increases heavily with age, more siblings in the family of origin, and better health. The family income, which is currently the focus of the literature and is statistically significant, is only sixth most important. This study further reveals differences between genders: Women with a lower level of education and religious beliefs prefer to have a second child, whereas for men, non-agricultural hukou and marriage are the position factors. The results of this study also illustrate the importance of future research focusing on the relationship of individuals to their family of origin and districts.