Doctor Who-The Face Of Evil
The new companion in question is Leela,member of a tribe called the Sevateem whom the doctor encounters while landing on a jungle planet by himself in the TARDIS. This tribe seem primitive. However the god they are worshiping leaves them in a near stone age style of life. and this "gods" face is carved in a nearby mountain side ala Mt.Rushmore. And it's...Tom Baker. Realizing that a sentient computer he created designed to guide the two warring tribes,the Sevateem and the Tesh,was the source of all this chaos he and Leela join forces to handle the situation. Turn out the Tesh are quite a bit more advanced. And her using this computer,who believes itself to still be the fourth doctor,for their own purposes. So the doctor now faces a cybernetic version of himself with an identity crisis and and overly eager new companion all at once.
In the end this is one of the more intellectually stimulating and less action/adventure type science fiction of all of Doctor Who. And this was a show that always balanced both very well. Here the doctor faces the consequences of his interference in another society and the cultural divisions it's created. Not only that but in facing his own consciousness via the computer being Xoanon he faces the darker side of his own nature. It culminates in one of the most powerful lines in the entire series: "The very powerful and the very stupid have one thing in common. They try to alter the facts to fit their views instead of altering their views to fit the facts. Which makes it very uncomfortable if you happen to be one of the facts that needs altering". That sums up the basic theme of the entire serial. Not only that but it's an emotionally simulating way of introducing Leela,a new and somewhat different type of companion.