A power extraction and amplification system for a gas turbine engine is disclosed. In various embodiments, the power extraction and amplification system includes a low spool tower shaft configured for engagement with a low speed spool, a high spool tower shaft configured for engagement with a high speed spool, a first motor, a generator, a differential gear box operably coupled to the low spool tower shaft, to the first motor and to the generator, and a second motor operably coupled to the generator and the high spool tower shaft.