The Second Doctor

Players have no maximum hand size.
How Civil of You — At the beginning of your end step, each player may draw a card. Each opponent who does can't attack you or permanents you control during their next turn.

Arcane Signet

{T}: Add one mana of any color in your commander's color identity.

Clockspinning

Buyback {3} (You may pay an additional {3} as you cast this spell. If you do, put this card into your hand as it resolves.)
Choose a counter on target permanent or suspended card. Remove that counter from that permanent or card or put another of those counters on it.

The First Doctor

When The First Doctor enters, search your library and/or graveyard for a card named TARDIS, reveal it, and put it into your hand. If you search your library this way, shuffle.
Whenever you cast a spell with cascade, put a +1/+1 counter on target artifact or creature.

The Fifth Doctor

Peaceful Coexistence — At the beginning of your end step, put a +1/+1 counter on each creature you control that didn't attack or enter this turn. Untap those creatures.

Cybership

Flying
Whenever Cybership deals combat damage to a player, put the top two cards of that player's library onto the battlefield face down under your control. They're 2/2 Cyberman artifact creatures.
Crew 4

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.)

Command Tower

Cybermat

Skulk (This creature can't be blocked by creatures with greater power.)
Whenever Cybermat attacks and isn't blocked, it gets +X/+0 until end of turn, where X is the number of attacking artifact creatures.

Bessie, the Doctor's Roadster

Haste
Whenever Bessie attacks, another target legendary creature can't be blocked this turn.
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.)

Adric, Mathematical Genius

{2}{U}, {T}: Copy target activated or triggered ability you control. You may choose new targets for the copy.
Ultimate Sacrifice — {1}{U}, Sacrifice Adric: Counter target activated or triggered ability.
Doctor's companion (You can have two commanders if the other is the Doctor.)