The troubled singer's signature tune, Rehab, is nominated for Best-Selling British Song.
And Love is a Losing Game, and You Know I'm No Good, are nominated for Best Song Musically and Lyrically -- the first time a singer has been twice-nominated for the honour since the awards were launched in 1955.
The latest nominations come two months after the London-based singer won five of the top prizes at the Grammy Awards in Los Angeles including best new artist, best pop vocal album, record of the year and song of the year for Rehab.
Also nominated for the Best-Selling British Song category is Grace Kelly, the song performed and co-written by Mika, and Beautiful Liar, the Beyonce and Shakira track written by Briton Amanda Ghost.
Radiohead's In Rainbows is nominated for best album. Foundations by London singer Kate Nash and Golden Skans by the Klaxons are also nominated for Best Contemporary Song.
The awards will be presented in London on May 22.