The Seventh Doctor

Whenever The Seventh Doctor attacks, choose a card in your hand. Defending player guesses whether that card's mana value is greater than the number of artifacts you control. If they guessed wrong, you may cast it without paying its mana cost. If you don't cast a spell this way, investigate. (Create a Clue token. It's an artifact with "{2}, Sacrifice this artifact: Draw a card.")

Osgood, Operation Double

When you cast this spell, create a token that's a copy of it, except it isn't legendary.
{T}: Add {C}. Spend this mana only to cast an artifact spell or activate an ability of an artifact.
Paradox — Whenever you cast a spell from anywhere other than your hand, investigate. (Create a Clue token. It's an artifact with "{2}, Sacrifice this artifact: Draw a card.")

Sarah Jane Smith

Whenever you cast a historic spell, investigate. This ability triggers only once each turn. (Artifacts, legendaries, and Sagas are historic. To investigate, create a Clue token. It's an artifact with "{2}, Sacrifice this artifact: Draw a card.")
Doctor's companion (You can have two commanders if the other is the Doctor.)

Clara Oswald

Impossible Girl — If Clara Oswald is your commander, choose a color before the game begins. Clara Oswald is the chosen color.
If a triggered ability of a Doctor you control triggers, that ability triggers an additional time.
Doctor's companion (You can have two commanders if the other is the Doctor.)

Nyssa of Traken

You have no maximum hand size.
Sonic Booster — Whenever Nyssa of Traken attacks, sacrifice X artifacts. When you sacrifice one or more artifacts this way, tap up to X target creatures and you draw X cards.
Doctor's companion (You can have two commanders if the other is the Doctor.)