Start the TARDIS

Surveil 2, then draw a card. You may planeswalk. (To surveil 2, look at the top two cards of your library, then put any number of them into your graveyard and the rest on top of your library in any order.)
Jump-start (You may cast this card from your graveyard by discarding a card in addition to paying its other costs. Then exile this card.)

Decaying Time Loop

Discard all the cards in your hand, then draw that many cards.
Retrace (You may cast this card from your graveyard by discarding a land card in addition to paying its other costs.)

The Fugitive Doctor

When The Fugitive Doctor enters, investigate.
Whenever The Fugitive Doctor attacks, you may sacrifice a Clue. When you do, target instant or sorcery card in your graveyard gains flashback {2}{R}{G} until end of turn. (You may cast that card from your graveyard for its flashback cost. Then exile it.)

Ryan Sinclair

Whenever Ryan attacks, exile cards from the top of your library until you exile a nonland card. You may cast the exiled card without paying its mana cost if it's a spell with mana value less than or equal to Ryan's power. Put the exiled cards not cast this way on the bottom of your library in a random order.
Doctor's companion (You can have two commanders if the other is the Doctor.)

Replication Technique

Demonstrate (When you cast this spell, you may copy it. If you do, choose an opponent to also copy it. Players may choose new targets for their copies.)
Create a token that's a copy of target permanent you control.

The Fourth Doctor

You may look at the top card of your library any time.
Would You Like A...? — Once each turn, you may play a historic land or cast a historic spell from the top of your library. When you do, create a Food token. (Artifacts, legendaries, and Sagas are historic.)

The Twelfth Doctor

The first spell you cast from anywhere other than your hand each turn has demonstrate. (When you cast that spell, you may copy it. If you do, choose an opponent to also copy it. A copy of a permanent spell becomes a token.)
Whenever you copy a spell, put a +1/+1 counter on The Twelfth Doctor.

Unlikely Meeting

Search your library for a Doctor card, reveal it, put it into your hand, then shuffle.

Twice Upon a Time

Cast this spell only if you control two or more Doctors.
Take an extra turn after this one. Exile Twice Upon a Time.

Twice Upon a Time // Unlikely Meeting

Bill Potts

Whenever you cast an instant or sorcery spell that targets only Bill Potts or activate an ability that targets only Bill Potts, copy that spell or ability. You may choose new targets for the copy. This ability triggers only once each turn.
Doctor's companion (You can have two commanders if the other is the Doctor.)

Quantum Misalignment

Create a token that's a copy of target creature you control, except it isn't legendary.
Rebound (If you cast this spell from your hand, exile it as it resolves. At the beginning of your next upkeep, you may cast this card from exile without paying its mana cost.)

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.)

Into the Time Vortex

Cascade (When you cast this spell, exile cards from the top of your library until you exile a nonland card that costs less. You may cast it without paying its mana cost. Put the exiled cards on the bottom in a random order.)
Rebound (If you cast this spell from your hand, exile it as it resolves. At the beginning of your next upkeep, you may cast this card from exile without paying its mana cost.)

Graham O'Brien

Paradox — Whenever you cast a spell from anywhere other than your hand, create a Food token. (It's an artifact with "{2}, {T}, Sacrifice this artifact: You gain 3 life.")
Doctor's companion (You can have two commanders if the other is the Doctor.)

Yasmin Khan

{T}: Exile the top card of your library. Until your next end step, you may play it.
Doctor's companion (You can have two commanders if the other is the Doctor.)

TARDIS

Flying
Whenever TARDIS attacks, if you control a Time Lord, the next spell you cast this turn has cascade and you may planeswalk.
Crew 2 (Tap any number of creatures you control with total power 2 or more: This Vehicle becomes an artifact creature until end of turn.)

The Thirteenth Doctor

Paradox — Whenever you cast a spell from anywhere other than your hand, put a +1/+1 counter on target creature.
Team TARDIS — At the beginning of your end step, untap each creature you control with a counter on it.

The Sixth Doctor

Time Lord's Prerogative — Whenever you cast a historic spell, copy it, except the copy isn't legendary. This ability triggers only once each turn. (Artifacts, legendaries, and Sagas are historic. A copy of a permanent spell becomes a token.)