No, when a Dashboard, Media, Thing, or other resource is added to the dashboard, it is bound to that particular resource. I believe this feature request is the closest - it’s focused on Thing tiles, but the same concept could apply to Dashboard or other resource types.
Can you help me better understand the use-case here? Why copy the same tile 4 times and then attempt to edit it? Why not just add the relevant dashboard tiles directly?
If it’s a styling thing, the suggested approach is to create a named style within a Theme, then you can easily reuse that style across your dashboard tiles.