When bilingual speakers switch back to speaking in their native language (L1) after having used their second language (L2), they often experience difficulty in retrieving words in their L1. This phenomenon is referred to as the L2 after-effect. We used the L2 after-effect as a lens to explore the neural bases of bilingual language control mechanisms. Our goal was twofold: first, to explore whether bilingual language control draws on domain-general or language-specific mechanisms; second, to investigate the precise mechanism(s) that drive the L2 after-effect. We used a precision fMRI approach based on functional localizers to measure the extent to which the brain activity that reflects the L2 after-effect overlaps with the language network (Fedorenko et al., 2010) and the domain-general multiple demand network (Duncan, 2010), as well as three task-specific networks that tap into interference resolution, lexical retrieval, and articulation. Forty-two Polish–English bilinguals participated in the study. Our results show that the L2 after-effect reflects increased engagement of domain-general but not language-specific resources. Furthermore, contrary to previously proposed interpretations, we did not find evidence that the effect reflects increased difficulty related to lexical access, articulation, and the resolution of lexical interference. We propose that difficulty of speech production in the picture naming paradigm—manifested as the L2 after-effect—reflects interference at a nonlinguistic level of task schemas or a general increase of cognitive control engagement during speech production in L1 after L2.