Do initiative bonuses stack?

Question

I am asking this specifically with regard to the bonus from Gift of Alacrity (if two different characters knew the spell and cast it on the same person), but if there is a general rule on stacking initiative bonuses, I'd like to know.

Answer 1

Spells and game features with the same name do not stack.

The "Combining Magical Effects" rule states:

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect — such as the highest bonus — from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.

So a character can only benefit from a single instance of gift of alacrity for a given roll. The Dungeon Master's Guide expands this rule to apply to all game features:

Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items. See the related rule in the “Combining Magical Effects” section of chapter 10 in the Player’s Handbook.

So if you had a non-spell game feature that gave a bonus to initiative rolls, you could only benefit from one instance of that particular feature.

Apart from these rules, there are no general restrictions on features stacking. If you have different features that effect the same initiative roll, they can all apply. The answers to this, How high can a PC's initiative bonus get?, question show how outrageous this can get, giving examples of numerous features working together to boost a single initiative roll.