Literal parameters and multiple users

Literal Parameters values are application-wide, session inspecfic.  Things like formats and colors work well in Literal parameters 

For user/session specific parameters, use Input Parameters:

In your code, these Input Parameters are oddly named "ModifiedSubVars".  You change the value of the ModifiedSubVars on the returned Task Result object, e.g.  XFLoadDashboardTaskResult, XFSelectionChangedTaskResult depending on what event you're handling.  Be sure to also set one or all of the ChangeCustomSubstVarsIn properties to True.

E.g. 

selectionChangedTaskResult.ChangeCustomSubstVarsInDashboard = True
selectionChangedTaskResult.ModifiedCustomSubstVars.Add("pm_myParameter_Name", "User Specific Value")

It finally works! The problem was that the popup came out every time the dashboard refreshed, thus every time this section of the script was triggered:

    Case Is = DashboardExtenderFunctionType.LoadDashboard
          If args.FunctionName.XFEqualsIgnoreCase("LoadFunction") Then
               .....
          End If

I managed to avoid the pop up to come out by adding a couple of lines of code:

 Case Is = DashboardExtenderFunctionType.LoadDashboard
          If args.FunctionName.XFEqualsIgnoreCase("LoadFunction") Then

            loadDashboardTaskResult.ChangeCustomSubstVarsInDashboard = True

            If Not(args.LoadDashboardTaskInfo.CustomSubstVarsFromPriorRun.XFGetValue("p_RowEntityList").Equals("None")) Then
            
            loadDashboardTaskResult.ModifiedCustomSubstVars.Add("p_RowEntityList", args.LoadDashboardTaskInfo.CustomSubstVarsFromPriorRun.XFGetValue("p_RowEntityList"))
            loadDashboardTaskResult.ModifiedCustomSubstVars.Add("p_RowAccList", args.LoadDashboardTaskInfo.CustomSubstVarsFromPriorRun.XFGetValue("p_RowAccList"))
            loadDashboardTaskResult.ModifiedCustomSubstVars.Add("p_RowDocList", args.LoadDashboardTaskInfo.CustomSubstVarsFromPriorRun.XFGetValue("p_RowDocList"))

            Return loadDashboardTaskResult

          Else

            loadDashboardTaskResult.ModifiedCustomSubstVars.Add("p_RowEntityList", "None")
            loadDashboardTaskResult.ModifiedCustomSubstVars.Add("p_RowAccList", "None")
            loadDashboardTaskResult.ModifiedCustomSubstVars.Add("p_RowDocList", "None")

            Return loadDashboardTaskResult

          End If
 End If

 The rest of the script is structured as Rob suggested.

Thank you all for the help!