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.)

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.)

Memory Worm

Paradox — Whenever you cast a spell from anywhere other than your hand, Memory Worm deals 2 damage to target player. That player discards a card, then draws a card. Put a +1/+1 counter on Memory Worm.

River Song's Diary

Imprint — Whenever a player casts an instant or sorcery spell from their hand, exile it instead of putting it into a graveyard as it resolves.
At the beginning of your upkeep, if there are four or more cards exiled with River Song's Diary, choose one of them at random. You may cast it without paying its mana cost.

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.)

Psychic Paper

As Psychic Paper becomes attached to a creature, choose a creature card name and a creature type.
Equipped creature has ward {1}, it can't be blocked, and its name and creature type are the last chosen name and creature type.
Equip {2}

Surge of Brilliance

Paradox — Draw a card for each spell you've cast this turn from anywhere other than your hand.
Foretell {1}{U} (During your turn, you may pay {2} and exile this card from your hand face down. Cast it on a later turn for its foretell cost.)

Bigger on the Inside

Enchant artifact or land
Enchanted permanent has "{T}: Target player adds two mana of any one color. The next spell they cast this turn has cascade." (When they cast their next spell, they exile cards from the top of their library until they exile a nonland card that costs less. They may cast it without paying its mana cost. They put the exiled cards on the bottom in a random order.)

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.)

Sonic Screwdriver

{T}: Add one mana of any color.
{1}, {T}: Untap another target artifact.
{2}, {T}: Scry 1. (Look at the top card of your library. You may put that card on the bottom.)
{3}, {T}: Target creature can't be blocked this turn.

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.)

The Flux

(As this Saga enters and after your draw step, add a lore counter. Sacrifice after VI.)
I — The Flux deals 4 damage to target creature an opponent controls.
II, III, IV, V — Exile the top card of your library. You may play that card this turn.
VI — Add six {R}.

Heaven Sent

(As this Saga enters and after your draw step, add a lore counter. Sacrifice after III.)
I, II — Investigate.
III — Heaven Sent deals 1 damage to each opponent. Then if an opponent has 0 or less life, draw seven cards. Otherwise, exile Heaven Sent and you may cast it this turn.

Sisterhood of Karn

Sisterhood of Karn enters with a +1/+1 counter on it.
Paradox — Whenever you cast a spell from anywhere other than your hand, double the number of +1/+1 counters on Sisterhood of Karn.

Search for Tomorrow

Search your library for a basic land card, put it onto the battlefield, then shuffle.
Suspend 2—{G} (Rather than cast this card from your hand, you may pay {G} and exile it with two time counters on it. At the beginning of your upkeep, remove a time counter. When the last is removed, you may cast it without paying its mana cost.)

Throes of Chaos

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.)
Retrace (You may cast this card from your graveyard by discarding a land card in addition to paying its other costs.)

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.")

Flaming Tyrannosaurus

Menace
Paradox — Whenever you cast a spell from anywhere other than your hand, Flaming Tyrannosaurus deals 3 damage to any target. Then put a +1/+1 counter on Flaming Tyrannosaurus.
When Flaming Tyrannosaurus dies, it deals damage equal to its power to each opponent.

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.

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.