Continuous measurement with 4200-SCS

You do have the older 4200-SCS running the KITE software.
More than 10 years ago, we transitioned to 4200A-SCS and Clarius software.
Keep in mind, there is always an upgrade path.  Contact your local sales office for more information.

For repeated execution of an ITM, check out the Reference Manual on enabling the cycle mode.
I believe max number of cycles is 128.  When running the cycle mode, the ITM test results will have a tab for each cycle.
This is similar to having multiple append tabs.  But cycle mode relieves you of some button pushing.

If cycle mode is not enough cycles, you might be able to use the Stress/Measure cycling and just pick a benign stress condition.

Alternately, you could close the KITE GUI interface and instead use external command interface (KXCI).  And then from another computer you can send commands over GPIB or LAN to do the repeated IV curves and read back the data.