While you can’t apply modifiers to object with linked data, nothing stops you from:
1 unlinking data in selected object (make single user)
2 applying modifier on selected object
3 relinking data from selected object to all with previously same data
4 copying modifiers from selected to all objects to remove double modifier effect
If that sounds like a lot of keypresses and menu searching for something like that logically should be one-two clicks then check out modifier list addon:
It also makes working on modifiers with object gizmos (empties) a lot easier:
Just note that by default ui is set to old style list (hence name of addon) so change it to stack.