There are two separate situations of mourning that (according to many opinions) require the tearing of a garment on the left side -- seeing the Kotel (or an ancient city in Judea) and the passing of a parent.

If one has performed kriah for one of those reasons and the second arises (multiple hypotheticals can be devised), does he tear again, or is the expression of mourning then inclusive of all reasons to mourn?

This site discusses multiple relatives (though not very clearly) but doesn't discuss the weightiness of differing reasons to tear.

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