The winners will be announced at the awards ceremony on February 4.
The 34-year-old SZA, born Solána Imani Rowe, snagged nominations for album of the year with SOS and record of the year and song of the year for Kill Bill while being shortlisted in multiple genres including pop, melodic rap and both progressive and traditional R&B.
The song Kill Bill, also nominated for best R&B performance, takes its name from the two-part Quentin Tarantino film with lyrics about killing an ex-boyfriend and his girlfriend.
The narrator concludes she would "rather be in hell than alone".
The album of the year nominees competing with SZA's SOS are Midnights by Swift, Endless Summer Vacation by Cyrus, World Music Radio by Jon Batiste, the record by boygenius, Did you know that there's a tunnel under Ocean Blvd by Lana Del Rey, The Age of Pleasure by Janelle Monáe and GUTS by Olivia Rodrigo.
Victoria Monét followed closely behind SZA with seven nominations including best new artist and record of the year and best R&B song for On My Mama.
Phoebe Bridgers, apart from her duo performance nomination along with SZA for Ghost in the Machine, scored six other nominations as part of boygenius, a collaboration with Julien Baker and Lucy Dacus.
Rodrigo took six nominations, with her hit vampire getting nominated for record of the year, song of the year and best pop solo performance.
Those six nominations tied her with country star Brandy Clark and industry stalwarts Eilish, Cyrus and Swift.
Swift has dominated headlines this year with her sold-out concert tour spectacular, the eponymous The Eras Tour movie documenting the shows, and her relationship with American football star Travis Kelce.
Although Swift failed to break away from the pack in nominations, those six give her 52 total for her career.
She has won 12 times.
Consistent with the girl power theme of this year's nominations, the motion picture Barbie, directed by Greta Gerwig, captured four of the five nominations for best song written for visual media category.
Among them was Eilish's What Was I Made For? which was also nominated for record of the year, song of the year and best pop solo performance.
Representing the guys, actor Ryan Gosling's I'm Just Ken got nominated in the visual media category.
Jon Batiste led male singers with six nominations.
This year's Grammys cover recordings that were released between October 1, 2022 and September 15, 2023.
The voters are recording artists, songwriters, composers, producers, mixers and engineers.
The awards ceremony will be televised live from Los Angeles on Sunday, February 4.
Last year pop icon Beyoncé won four Grammys, breaking the record for most career wins with 32.
She is also tied with her husband, rapper Jay-Z, with the most career nominations with 88.
