Panharmonicon

If an artifact or creature entering causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.

Suture Priest

Whenever another creature you control enters, you may gain 1 life.
Whenever a creature an opponent controls enters, you may have that player lose 1 life.

Elesh Norn, Mother of Machines

Vigilance
If a permanent entering causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.
Permanents entering don't cause abilities of permanents your opponents control to trigger.