NickOfTime's answer provides the general rule. Under usual circumstances, the initiative order remains fixed once it is set. However, there are a few exceptions.
Sphinxes can force initiative rerolls.
One of the Sphinx's Lair Actions (e.g. the androsphinx or gynosphinx):
On initiative count 20 (losing initiative ties), the sphinx can take a lair action to cause one of the following magical effects; the sphinx can’t use an effect again until it finishes a short or long rest:
- The flow of time is altered such that every creature in the lair must reroll initiative. The sphinx can choose not to reroll.
A mount's initiative can change mid-combat.
If you mount a horse or other controlled mount after initiative has been set, the mount's initiative changes to match the rider's:
The initiative of a controlled mount changes to match yours when you mount it.
A likely ill-advised use of the wish spell.
One of the listed uses of the wish spell may allow you to force an initiative reroll:
You undo a single recent event by forcing a reroll of any roll made within the last round (including your last turn). Reality reshapes itself to accommodate the new result. For example, a wish spell could undo an opponent's successful save, a foe's critical hit, or a friend's failed save. You can force the reroll to be made with advantage or disadvantage, and you can choose whether to use the reroll or the original roll.
I say that it may allow you to use wish on an initiative reroll because it says "last round" and technically initiative rolls happened before the round structure was put into place.