Like the title :) 

Not a situation where there are two women and they both swap souls / bodies, but something similar:

  • The Legends - The FL dies, but a couple things happen and the FL ends up being resurrected... except that her body is connected to another woman. When that woman is harmed, the FL is harmed in the same way. The FL is also invisible during the day, and when she becomes visible at night, she has the appearance of the other woman.
  • Alchemy of Souls - The FL is a mage with the power to swap bodies / souls. She tries to do so with one woman, but is interrupted by another woman, who is blind. Her soul ends up getting pulled into the blind woman's body. Unbeknownst to the FL, that blind woman's soul remains - so their souls are sharing the blind woman's body.
  • A Familiar Stranger - The female villain uses magic to swap faces with the FL, but they each keep their original bodies. 
  • Jun Jiu Ling - The FL is sentenced to death. Her best friend (her teacher's daughter) takes her place and dies in a fire so that the FL is believed to be dead. The FL's teacher uses a special technique to change the FL's face and voice so she looks and sounds like her best friend / her teacher's daughter.
  • The Eternal Love - The FL lives in modern times, until her soul travels back in time and ends up in the body of the SFL. The SFL's soul / consciousness remains - but only one of them (the FL and the SFL) is conscious and in control of the SFL's body at any given time. 
  • Moon Lovers: Scarlet Heart Ryeo - The FL lives in modern times, until her soul travels back in time and ends up taking over the body of a noblewoman. The FL's soul doesn't seem to be sharing the noblewoman's body with the soul / consciousness of the noblewoman. 
  • Till the End of the Moon - The FL is an immortal cultivator. After a disaster occurs, the FL's soul travels 500 years into the past and takes over the body of the ML's wife, who is mortal. The FL's soul doesn't seem to be sharing the mortal woman's body with the soul / consciousness of the mortal woman.
  • The Romance of Tiger and Rose - The FL writes scripts for historical dramas in modern times, until she wakes up inside the world of one of her scripts and in the body of the character who is supposed to be the SFL. The FL's soul doesn't seem to be sharing that body with the soul / consciousness of the character she replaced.

 Irresistible Love (basically Freaky Friday: a girl and her mom swap bodies, meaning the daughter goes to work and the mom to school)

and maybe...

As Gentle as You (FL bodyswaps with an stranger who is an actress but the drama doesn't show her since it follows the FL's story)

  • Please Come Back, Soon Ae - not really a good drama but it has the plot.
  • Otto no Kanojo