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Mr Clever attempted to take over the Eleventh Doctor's mind when trying to convert him into a Cyberman. The mind was subsequently split into two halves; 49.881% in the Doctor's control and 49.881% under Mr Clever's influence. The two sides differentiated, with Mr Clever's half coloured silver and blue with circuitry scattered around, while the Doctor's was orange with Gallifreyan symbols covering it. (TV: Nightmare in Silver)
Within the mind, the Doctor could apply a mental block to prevent intruders from seeing things he did not want them to see. (TV: New Earth, Nightmare in Silver) However, if the Doctor was purposefully connecting with another, namely Jeanne-Antoinette Poisson with the Tenth Doctor, they could see into his memories, so long as the Doctor maintained the connection. (TV: The Girl in the Fireplace) Once, the Eleventh Doctor rapidly connected his mind with Craig Owens' to speedily share information, although the process resulted in a mild headache. (TV: The Lodger)
Regeneration energy could also transfer the knowledge within the Doctor's mind to another. Donna Noble gained the Tenth Doctor's mind by touching his severed hand while it was infused with regeneration energy from a recent regeneration. However, given she was human, the Tenth Doctor had to remove all memory of himself from her soon after to ensure her mind did not burn from trying to possess a Time Lord consciousness. (TV: Journey's End)
The Twelfth Doctor could willingly enter his mind to quickly deduce problems when under extreme duress. While there, his mind took the image of his TARDIS while he worked out solutions. Given how quickly his mind processed information, what seemed like minutes to him was mere seconds outside his mind. (TV: Heaven Sent)