Now that I'm set on the EQE 500, I've started looking around for whatever details I can find from people who already have it. While searching around mbusa, I happened upon the Mercedes me connect store and found this little tidbit:

Mercedes-EQ EQE 350 4MATIC from 215 kW to 260 kW from approx. 6.0 seconds to approx. 5.1 seconds

They also list the SUV and the 450, but notably the EQE 500 and EQS 580 don't have an upgrade available.