There is no 'line' level configuration option to do what you are asking. This is one of those things that Cisco wants you to do with partitions and calling search spaces.
Essentially, you set up a partition called PrivateCaller_PT and a search space called PrivateCaller_CSS.
Create a translation that matches your internal dialplan, say 4XX if you only have 3digit extensions that start with 4, and in the calling party transformation parameters Calling Line ID Presentation & Calling Name Presentation set to Restricted.
This will achieve what you are looking for, in principle, anyways.
In the past you would have to add additional translation patterns with more precise DNs to 'not block' calling ID to specific numbers, i.e. security, however, they have added the "Ignore Presentation Indicators (internal calls only)" parameter on the device which will ignore the translation pattern.
You wil find that you will be doubling up on your calling search spaces in order to achieve this. For example, if you have 6 calling search spaces for your area, you have the potential of someone in each calling search space not wanting to display their calling ID.
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