Alexander Masibaka, who plays in France's second division with Soyaux-Angouleme, has also been added.
Hastings sustained a fractured jaw playing for Glasgow against Scarlets in the autumn but made his return to club rugby earlier this mon
Back-rower Mann was involved in the build-up to Scotland's first three matches in the tournament but missed last week due to a concussion sustained playing for Glasgow Warriors against Ospreys.
Steyn has been absent since January with a knee injury, but Glasgow's captain will "continue his recovery" with the national team.
Leicester Tigers lock Cameron Henderson, Sale Sharks wing Arron Reed, Bath centre Cameron Redpath and Northampton Saints centre Rory Hutchinson all drop out of the squad and return to their clubs having not featured in the tournament.