I am assuming that you have Embedded PRI on this system.
In the Setup of the PRI there are 3 "Call by Call" vaiables available. One for Bearer Capabilities, one for Network Facilities and One for Calling ID Restriction.
If the CLIR is set to Call by Call, then you can use the modified digit entry to select whether to send the calling line ID or not.
I typically setup my ARS to have 2 methods of dialing out. onw with CLIR on and one with CLIR off.
In my area the standard residential code for blocking ID is *67. I therefore setup my ARS with *67 as the leading digits instead of 9.
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Occam's Razor - All things being equal, the simplest solution is the right one.