Firstly, I'd like to say that while this method will allow the machine to create a finer grind, in the process, we will remove the safety systems that protect the grinder from damaging itself. Modifying the grinder in this way can damage your grinder and will likely void the warranty (if there is one). After completing this modification, be well aware of the distance between the burrs before you start grinding.
My current opinion is that the even after completing this procedure, this grinder is not capable of producing a good espresso grind. However, it will produce a grind much finer than what it is natively capable of.
This method uses two step approach. In the first step we remove the physical barrier preventing the hopper to turn past the finest grind level. In the second step, we disable the electronic control that stops the grinder from turning on when the bean hopper is turned past the finest grind level.
Step 1: Cut the Plastic Tabs
Step 2: Open Up the Machine - Pt. 1
To open the machine, the first step is to flip the grinder over and unscrew the four screws on the bottom of the machine. These are hidden by the four rubber feet in each corner. Remove each rubber foot, then use a phillips head screwdriver to unscrew each screw. Remove the bottom, being careful of the power cord. The third image is the machine flipped upside down with the bottom cover removed. You'll see some electronics on the bottom of the picture, and the grinder motor is in the center of the machine. We don't have to deal with either of these.
Step 3: Open Up the Machine - Pt. 2
Step 4: Open Up the Machine - Pt. 3
The second picture shows the circular cover removed. You'll see several springs; one of them (see image) is part of the second electronic safety switch.
Step 5: Disable the Electronic Safety Switch
When the hopper is in one of the defined grind settings, a large semicircular plastic tab on the hopper which fits into the the circumferential groove pushes the switch activator into the switch housing allowing the grinder to turn on. When the hopper is turned past the finest grind setting, the tab no longer pushes the switch activator into the switch housing, allowing the spring to force the switch activator out of the switch housing and disabling the grinder.
Since the machine can be turned on only when the switch activator is inside the switch housing, the solution is to always have the switch activator in the switch housing.
Removing the spring and glue the switch activator into the switch housing (see the first picture).
Step 6: Put the Machine Back Together and Enjoy!
Your machine should now be able to grind much finer than originally! Again I stress that care is required to make sure that the burrs do not touch. All of the built in safety mechanisms that normally stop the burrs from grinding against each other have been removed. The instructable "Hacking the Cuisinart SupremeGrind for Espresso" gives good instruction on how to check the distance between the burrs.
To to make the grind finer, turn the hopper past the finest grind setting and turn the machine on.