Yes, it is possible to be rewarded multiple times in a single era. The rewards are organized and distributed by validator, so if a nominator's stake is split between multiple validators in an era, there will be one reward event per validator for that era.
However, this will only occur if the stake is split between multiple validators, and this usually only happens when a user has a very large amount at stake, and the staking algorithm decided to split that stake in order to keep the amount at stake for each validator as even as possible. This is one of the goals of the Phragmen algorithm used in the NPoS system.
EDIT: I found an example for you by looking at accounts with a large DOT balance:
Here you can see the user was rewarded multiple times in the same era from different validators because their stake was split among them.