The resolution on this one turned out to be to verify the permissions on the "~/Library/Application Support/IBM/SPSS Statistics/one" directory. This is the default location for Extensions, Custom Dialogs, Python3 and R instances. In this case, the "~/Library/Application support/IBM" existed, but it was owned by root and had permissions set only for root:
drwx------ 3 root staff 96 Jun 13 07:08 IBM
We reset the permissions to Robert and allowed others to read and execute:
drwxr-xr-x 3 robert staff 96 Jun 13 07:08 IBM
At that point the entire "~/Library/Application Support/IBM/SPSS Statistics/one" directory structure and contents were successfully created and populated, allowing the third party PROCESS v5.0 extension bundle to be installed and used.