Cast the self-suspending card by paying its mana cost if its in your hand, or any other spell otherwise if you have not cast a spell this turn.
Cast Twice Upon a Time by paying its mana cost.
Taigam triggers, copying Twice Upon a Time and then exiling it with four time counters on it and giving it suspend.
Resolve the copy of Twice Upon a Time, causing you to take an extra turn after this one.
Move to your next turn. At the beginning of that turn's upkeep, Twice Upon a Time and the self-suspending card's suspend abilities trigger, removing a time counter from each of them.
Activate The Tenth Doctor by paying {7}, removing three time counters from Twice Upon a Time and the self-suspending card, triggering their suspend abilities.
Resolve the self-suspending card's suspend trigger, causing you to cast it from exile without paying its mana cost, and eventually exile it with time counters on it.
Resolve the Twice Upon a Time's suspend trigger, causing you to cast it from exile without paying its mana cost.
Repeat from step 3.

Infinite turns

Lock

Self-Suspending Instant or Sorcery

The Tenth Doctor

Taigam, Master Opportunist

Twice Upon a Time // Unlikely Meeting

Cast Twice Upon a Time by paying its mana cost.
Taigam triggers, copying Twice Upon a Time and exiling the original Twice Upon a Time with four time counters on it.
Resolve the Twice Upon a Time copy, causing you to take an extra turn after this one.
Cast Clockspinning with buyback by paying {3}{U}, removing a time counter from Twice Upon a Time and returning Clockspinning to your hand.
Repeat step 4 one additional time.
Move to your next turn. At the beginning of your upkeep, Twice Upon a Time's suspend ability triggers, removing a time counter from it.
Cast Clockspinning with buyback by paying {3}{U}, removing a time counter from Twice Upon a Time and returning Clockspinning to your hand.
Twice Upon a Time's suspend ability triggers, causing you to cast it from exile without paying its mana cost.
Repeat from step 2.

Clockspinning

At the beginning of your upkeep, Panoptic Mirror triggers, casting a copy of Twice Upon a Time without paying its mana cost.
Resolve Twice Upon a Time, causing you to take an extra turn after this one.
Repeat each turn.

Panoptic Mirror

Cast Twice Upon a Time by paying {4}{U}{U}.
Riku's first ability triggers - choose not to pay.
Holding priority, cast Narset's Reversal by paying {U}{U}, targeting Twice Upon a Time.
Riku's first ability triggers, causing you to pay {U}{R} to copy Narset's Reversal, with the copy targeting the original Narset's Reversal.
Resolve the copy of Narset's Reversal, copying the original Narset's Reversal targeting Twice Upon a Time, and returning the original Narset's Reversal to your hand.
Resolve the copy of Narset's Reversal created in step 5, copying Twice Upon a Time and returning the original Twice Upon a Time to your hand.
Resolve Twice Upon a Time, causing you to take an extra turn after this one.
Repeat each turn.

Riku of Two Reflections

Narset's Reversal

Declare Fire Lord Azula as an attacker, triggering its firebending ability, adding {R}{R}.
Holding priority, cast Twice Upon a Time // Unlikely Meeting by paying its mana cost.
Fire Lord Azula's second ability triggers, copying Twice Upon a Time // Unlikely Meeting.
Holding priority, cast Narset's Reversal by paying {U}{U}, targeting the original Twice Upon a Time // Unlikely Meeting spell.
Fire Lord Azula's second ability triggers, copying Narset's Reversal, targeting the original Narset's Reversal.
Resolve the copy of Narset's Reversal, causing you to copy Narset's Reversal targeting the original Twice Upon a Time // Unlikely Meeting spell, and then return the original Narset's Reversal to your hand.
Resolve the copy of Narset's Reversal, copying Twice Upon a Time // Unlikely Meeting and returning the original Twice Upon a Time // Unlikely Meeting to your hand.
Resolve both copies of Twice Upon a Time // Unlikely Meeting from steps 3 and 7, causing you to take two extra turns after this one.
Repeat during your second extra turn.

Fire Lord Azula

Valley Floodcaller

Deal combat damage to an opponent using Efreet Flamepainter.
Efreet Flamepainter triggers, causing you to cast Unlikely Meeting from your graveyard without paying its mana cost.
Resolve Unlikely Meeting, causing you to take an extra turn after this one and exile it.
Activate Isochron Scepter by paying {2} and tapping it, casting a copy of Pull from Eternity without paying its mana cost.
Resolve Pull from Eternity, putting Unlikely Meeting from exile into your graveyard.
Repeat each turn.

Combos with "Twice Upon a Time // Unlikely Meeting"