Mirror of a mirror?

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Hi -
I have a model that is a square plate with five features in the top right corner. I want to mirror horizontally and vertically so that the features appear (mirrored) in all four corners. The features are asymmetrical, so I can't just copy them; they need to be mirrored.
I made a selection set of the five features. I can then easily mirror them to the bottom right corner or the top left corner. But what about the bottom left corner? I tried to select the already created top left mirror feature in the mirror tool, but it is not select-able there.
After some trial and error I came up with a solution but a) it is messy and b) it does not seem always to work:
1) Make a selection set of the five features.
2) Mirror to the top left corner. Use the selection set to fill in the "features to be mirrored" box.
3) Make a new selection set of the original five features and also the new mirror feature from the timeline.
4) Mirror to the two bottom corners using this new selection set.
I often do this: mirroring twice to get a component with horizontal and vertical symmetry. Is there a simpler and more reliable way to accomplish this in F360?
I have not explored this further but wonder if this is a general issue when making copies of copies, patterns of patterns, copies of mirrors, etc.
Any suggestions appreciated...
- MWoll