@Phillip_Le - Thanks for your response. Based on your explanation, I believe now I have got the problem clearly. Can you please check the below step by step implementation thoughts process and let me know if this is what you are looking for.
Sample Dataset Snippet that I have used for the POC. Here I will try to have name = specific always selected in the background and when any other name(s) will be selected from the slicer, then all the records having name = slicer selection will be shown in addition to the records qualifying the criteria name = specific.
Step 1 : Create a Parameter named paramName
Step 2 : Create an “OR” Filter based on that “name” column
Step 3 : Modify the Control to configure it as List - Multiselect and in the value specification put all the values except “specific” which you don’t want to appear in the slicer selection to appear
Step 4 : Sample Run
Did my suggestion help you in resolving your query? If yes, would request you to mark the post as “Solution”. This will help the community to find guidance and answers to similar question. Thank you!