We report the results of a study into the feasibility of conducting the ELISE and EXL experiments on collisions of nuclei of radioactive fragments with electrons at the Institute for Theoretical and Experimental Physics (ITEP). A scheme for uranium ion acceleration in the ITEP accelerator complex is chosen, and it is shown that uranium ions may be accelerated with an intensity of ∼1 × 1011 ions/s as soon as the complex is modified and a new injector is constructed. The basic parameters of the modified complex are given, and a layout diagram indicating the positions of the target that serves to produce radioactive fragments, the separator, and the storage rings (CR, RESR, NESR, and ER) at the ITEP site is presented.