The user can split or divide their own soul or the souls of others to create new beings, including basing the division on personalities and emotions to become separate beings, as well have the divided portions to possess other people. They can even achieve immortality by sealing fraction of their soul in certain objects and having them anchor the "main" soul onto the earth should the body be destroyed.
Coyote Starrk/Lilynette Gingerbuck (Bleach) can split their soul apart for companionship and wolf-based attacks.
Szayelaporro Granz (Bleach) split his soul off to create his brother Ilfort Granz via experiment, thus devolving from a Vasto Lorde back into an Adjuchas.
Nemu Kurotsuchi (Bleach) using Konpaku Sessaku to split off 6% of her soul to fire off the Gikon Jūrinjū, a devastating projectile that easily pierced Pernida.
Yhwach (Bleach) is able to split his soul and distribute the portions to others.
In order to help her control her immense power, Belial Aensland (Darkstalkers) split Morrigan's soul into three fragments, sealing one portion of it in himself...
...while the second portion eventually gained its own body and conscious mind, becoming Lilith.
Due to his soul's instability after having his body changed so many times, Alphonse Elric (Fullmetal Alchemist 2003) gained the ability to split his soul into pieces and insert them into inanimate objects to act as golems.
Voldemort (Harry Potter) split his soul into eight fragments and placed seven of them into special Horcruxes to achieve a form of immortality but at the cost of his mental, physical and spiritual instability.
Master Xehanort (Kingdom Hearts) split his heart and essence into fragments and implanted them into twelve different individuals to convert them into his clones.
Ryō Bakura (Yu-Gi-Oh!) splitting a portion of his soul and implanting them into his dice, ensuring he will roll a super critical.
Kain (Legacy of Kain) revived his six lieutenants as vampires by splitting off portions of his soul and breathing them into their corpses.
Charlotte Linlin/Big Mom (One Piece) used fragments of her own soul to create her three personal homies, Prometheus, Zeus and Napoleon.
Carmel (One Piece) separates a piece of her soul...
...and infuses it into an inferno to create Sun Homie Pandora.
Minato Namikaze (Naruto) use the Reaper Death Seal to split Kurama/Nine-Tails' spirit into yin and yang, sealing the yin half into himself and the yang half into his son, Naruto Uzumaki.
Vergil (Devil May Cry) used Yamato to split his soul into two...