I used the following procedure to program a third key for my 2009 Caravan (cut & pasted from the first edition 2009 Caravan pdf manual):
Customer Key Programming
If you have two valid RKE transmitters with integrated
keys, you can program new RKE transmitters to the
system by performing the following steps:
1. Insert the first valid integrated key into the ignition
switch and turn the ignition switch to the ON position for
at least three seconds, but no longer than 15 seconds.
Turn the ignition switch to the LOCK position and
remove the first key.
2. Insert the second valid integrated key and turn the
ignition switch to the ON position within 15 seconds.
After 10 seconds, a chime will sound and the Vehicle
Security Light will begin to flash. Turn the ignition switch
to the LOCK position and remove the second key.
3. Insert a blank integrated key into the ignition switch
and turn the ignition switch to the ON position within
60 seconds. After 10 seconds, a single chime will sound
and the Vehicle Security Light will stop flashing, turn the
ignition switch ON again for three seconds, and then turn
The new integrated key is programmed. The Remote
Keyless Entry (RKE) transmitter will also be programmed
during this procedure.
Repeat the above steps to program up to eight keys. If
you do not have a programmed RKE transmitter with
integrated key, contact your authorized for details.
There was something that didn't work exactly like the instructions, I think maybe there was no chime at step 2, but I can't remember for certain.
For some reason this section of the manual was removed from later editions of the manual.