Cancers show considerable genetic and functional heterogeneity, preventing the development of a universal anticancer drug. Here, I argue that it is nevertheless possible to elaborate a therapeutic strategy that can be used in almost every cancer, exploiting the negative feedback effect of normal cells on the proliferation of their precursors. This method, termed cell inflation assisted chemotherapy, is aimed at blocking normal cell division prior to high-dose antimitotic chemotherapy. Evidence for a negative feedback effect on granulocyte production suggests that it is possible to prevent neutropenia by transfusion of autologous granulocytes. In a first step, this protocol will be devised to protect neutrophils and to prevent granulopenia in patients treated with intensive chemotherapy. In its simplest form, it will consist of a leukapheresis–storage–reinjection sequence just prior to drug administration. Then, if the proof of concept is established, a more systematic use of intensive cell cycle-specific chemotherapy, together with protection of other lineages through temporary mitotic blockade might be a treatment applicable for most cancers.