Facelift (LCI) Cooper Ds and all Coopers SDs have BMW diesels and they don't have an additive tank.
Though we are in danger of mixing up the subjects of factory-fitted EOLYS tank (which is there to keep the DPF in good order, on Peugeot engines) and diesel fuel tank additives (which are sold to supposedly improve engine condition/performance). Independent tests do not seem to show that diesel fuel tank additives do any good - or at least no more good than the same value of diesel fuel.