There are two types of set item bonuses - individual item bonuses that only apply if you are wearing multiple different items in a set, and the full set bonus, which only occurs if you are wearing every item in the set.
You will not receive the full set bonus twice if you are wearing something like Cathan's Traps or Angelic Raiment - however, you will receive whatever individual item bonuses those pieces contribute.
For this reason, two Angelic rings and the amulet are very popular for melee characters, as Angelic Wings (the amulet) gives
+75 life with 2 items and Angelic Halo (the ring) gives
+3 to Attack Rating per Clvl (for a total of
+6 to Attack Rating per Clvl with two rings). Adding either Angelic Mantle (the ring mail) or Angelic Sickle (the sabre) means you get the three item bonus off the rings as well, so the
+50% Magic Find per ring means a both
+100% Magic Find and
+6 to Attack Rating per Clvl.