Stratified biomedicalization (Clarke et al., 2003, 2010) is a notion derived from Science and Technology Studies (STS) that refers to the complex ways in which biomedical implementations are distributed, often unintentionally, in an uneven manner between people because of their social class, gender, ethnicity, or race, which aggravates health inequities. Hence, although it is suggestive, the category is inadequate when considering the Global South. In this chapter I point out the limitations of this notion and suggest the concept of aspirational biomedicalization with the purpose of showing how stratification joins the aspirations of the government to apply public policies from the Global North, which affect those who receive said policies. This conceptual proposal stems from my empirical work done in Mexico about the sociotechnical complexities of the implementation of public policies regarding preventive vaccination against human papillomavirus (HPV) and pre-exposure prophylaxis (PrEP) to prevent human immunodeficiency virus (HIV). Thus, in this text I offer a theoretical alternative to critically consider the way in which social contexts of the Global South can contribute to the creation of new concepts for STS.