Immunomodulatory imide drugs (IMiDs) bind CRBN, a substrate receptor of the Cul4A E3 ligase complex, enabling neo-substrate recruitment and degradation via the ubiquitin-proteasome system. Here, we report FAM83F as such a neo-substrate. We recently showed that the eight FAM83 proteins (A-H) interact with members of the serine/threonine protein kinase CK1 family, to regulate their subcellular distribution and distinct biological roles. CK1α is a well-established IMiD neo-substrate and we demonstrate here that IMiD-induced FAM83F degradation requires its association with CK1α. Despite all FAM83 proteins interacting with CK1α, no other FAM83 protein is degraded by IMiDs. FAM83F is localised to the plasma membrane, and consistent with this, IMiD treatment results in depletion of both FAM83F and CK1α levels from the plasma membrane. We have recently identified FAM83F as a mediator of the canonical Wnt signalling pathway. The IMiD-induced degradation of FAM83F attenuated Wnt signalling in colorectal cancer cells and removed CK1α from the plasma membrane, mirroring the phenotypes observed with genetic ablation of FAM83F. Intriguingly, in many cancer cell lines, IMiD-induced degradation of CK1α is only modest and incomplete. In line with this observation, the expression of FAM83G, which also binds to CK1α, appears to attenuate the IMiD-induced degradation of CK1α, suggesting a protective role for FAM83G on CK1α. Our findings reveal that the efficiency of target protein degradation by IMiDs, and perhaps other degraders such as PROTACs, relies on the nature of the inherent multiprotein complex in which the target protein exists. Our findings unearth opportunities for developing degraders to target specific protein complexes.