This is achievable, you need to have the following things in place.
The master CI record, with the field that you want to update on it.
The field needs to match all of the CI's.
The master CI does not have to be the same item type.
You need to have all of the items you want to be updated each time to be linked to this master CI.
You would then need a rule configured on the side where the CI's exist that you want updated en masse.
This rule would run on the Linked Item update trigger, that captures the change on the master CI side, and then changes the record on the item side of the CI's needing the update. If you are looking at dozens, hundreds, or even more CI's linked to this one master CI, you should make this a timer rule, not an on update rule because you will choke up the system trying to run this rule on thousands of items at once.
You should consider some controls in this rule as well, that would prevent it from running more than once per update of the master CI field. There are many ways to do this, but this way is ideal.