1. If I have two Shifting Shadows out on the battlefield on two different creatures what happens on my next upkeep?
2. What happens if I equip the same creature twice?
1. In this case, the ability of each Shifting Shadow you control will trigger. Since you control both of them, you may put them on the stack in any order (C.R. 116.5, 603.3b).
2. I assume you mean "enchant" rather than "equip". My answer to question 1 applies even if both Shifting Shadows are attached to the same creature. When the ability of each resolves, as much of its instructions as possible are followed even if the creature has left the battlefield (for example, if it was destroyed while a previous Shifting Shadow ability resolved) (C.R. 608.2c, 609.3).
If you control the creatures enchanted by Shifting Shadow, then on your upkeep, you resolve the effect of one Shifting Shadow's trigger. Some cards move in the library and Shifting Shadow attaches to a new permanent. Then you resolve the effect of the other Shifting Shadow.
If you don't control those creatures, then on your upkeep you haven't pointed to any reason for something to happen.
If one creature is enchanted by two Shifting Shadow, then when the first of those abilities resolve, it will do as it says, and then the other Shifting Shadow is put into the graveyard as a State-Based Action. Then the other triggered ability resolves, except when the new permanent appears, Shifting Shadow can't be attached to it because it is not in the expected place (on the battlefield).
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2. What happens if I equip the same creature twice?
2. I assume you mean "enchant" rather than "equip". My answer to question 1 applies even if both Shifting Shadows are attached to the same creature. When the ability of each resolves, as much of its instructions as possible are followed even if the creature has left the battlefield (for example, if it was destroyed while a previous Shifting Shadow ability resolved) (C.R. 608.2c, 609.3).
If you don't control those creatures, then on your upkeep you haven't pointed to any reason for something to happen.
If one creature is enchanted by two Shifting Shadow, then when the first of those abilities resolve, it will do as it says, and then the other Shifting Shadow is put into the graveyard as a State-Based Action. Then the other triggered ability resolves, except when the new permanent appears, Shifting Shadow can't be attached to it because it is not in the expected place (on the battlefield).
Awesome avatar provided by Krashbot @ [Epic Graphics].