Corporelectroscopy

Corporelectroscopy was the process by which two (or more) people switched their minds into each others' bodies. It could also allow one mind to take over another completely, enabling one brain to move into another individual's body, effectively taking control and killing the other.

The Javaman, a scientist with considerable imagination, called corporelectroscopy a "scientific implausibility". He was unaware that the theta-waves emitted by his Dorganator had caused the process to occur with the Sixth Doctor and Peri Brown. The Doctor later told Peri that corporelectroscopy was dangerous knowledge, and that it was "best left to the Time Lords". (PROSE: Turnabout is Fair Play)

The Great Architect Kroagnon "discovered a means of performing" corporelectroscopy to transplant his brain into the Chief Caretaker of Paradise Towers. This brought about physical changes in the Chief; while Kroagnon now had a body, he walked stiffly, spoke as though his tongue was swollen, his skin took on a silvery colour, and his moustache grew. (TV: Paradise Towers)

Similar processes
Body swapping was possible in the Sol system by 2109. Kadiatu Lethbridge-Stewart agreed to let Max have six hours "walking around in" time in her body if she didn't repay his loan after three months. (PROSE: Transit)

In 2379, Crozier developed a method that allowed the Mentor Kiv to successfully take over Peri's body, and would allow him to continue taking over bodies and essentially become immortal. The High Council of the Time Lords manipulated Yrcanos as an assassin to stop Crozier and Kiv, as this discovery would upset the natural flow of evolution. (TV: Mindwarp)

In the far future, the banned psychograft allowed one mind to take over another body, with the former's body being destroyed. The overtaken mind would still exist but be slowly compressed to death. (TV: New Earth)