Adele's YouTube-shattering video for her 2015 comeback single Hello notched seven nominations, while the sultry British singer earned an eighth mention for Send My Love (To Your New Lover).
The controversial video for West's Famous - which features portrayals of 12 nude celebrities including Swift sleeping next to the rapper - got two nominations, including the top award of video of the year.
Swift and West have been publicly feuding for months about whether the pop star approved lyrics in which West boasts about making her famous.
Swift, 26, the top-earning celebrity in the world, has dominated music awards shows in the past five years and won four MTV music video prizes in 2015, including for her single Bad Blood with Kendrick Lamar.
