Xjyuk

I was trying to figure out if a tiefling could have more than two horns. The PHB doesn't specifically state how many horns they can have and most depictions just have two so I wasn't sure if that was the max.

Can a Tiefling have more than two horns or is two the max?

PHB 40, Tieflings:

generations ago infused the essence of
Asmodeus — overlord of the Nine Hells — into their
bloodline. Their appearance and their nature are not
their fault but the result of an ancient sin

[...]

Tieflings have large horns that take any
of a variety of shapes: some have curling horns like a
ram, others have straight and tall horns like a gazelle’s,
and some spiral upward like an antelopes’ horns.

DMG 66, Asmodeus:

Asmodeus most often appears as a handsome,
bearded humanoid with small horns protruding from
his forehead, piercing red eyes, and flowing robes.

In neither of these entries, any number of horns is specified, the most significant read on the number of horns is the use of plural which indicates more than or exactly two horns, but doesn't strictly abide by that.

If you wanted to play/create a horn- or tailless Tiefling without forgoing the wording, then this thread may be of interest to you and the implied consequences thereof Can a Tiefling self-mutilate to remove their horns/tail, and if so, does it do damage?

The most common depiction of Tieflings is the goat variety that has two horns. PHB 42, and 103.
The noted animals vary from being hornless, one-horned, two-horned, four-horned, six-horned, and eight-horned.

Multiple horns or no horns are technically allowed.

Tieflings in D&D 5e are described as having an unspecified number of horns, and while it is generally implied to be two horns and depicted so in art, this isn't strictly defined. It's also a valid variant to have no horns.

Multiple horns, but usually two

Player's Handbook p.42 notes:

Their hair, cascading down from behind their horns [...]

This implies that a tiefling's horns are located at the front of their head, and that a tiefling has multiple horns, most likely two. However, it doesn't strictly say "two horns", "a pair of horns", or the like, only that they have:

large horns that take a variety of shapes

It is therefore valid, by the wording of the rules, for a tiefling to have more than two horns. However, the rules do not appear to leave an opening for one-horned tieflings.

In older editions of the game, Asmodeus himself is usually depicted as having exactly two horns. This implies that tieflings should probably have two horns.

No horns

However, some tieflings have no horns. Sword Coast Adventurer's Guide p. 118, under the Tiefling Variants sidebar notes:

Since not all tieflings are of the blood of Asmodeus, some have traits that differ from those in the Player's Handbook. [...]

Appearance. Your tieflings might not look like other tieflings. Rather than having the physical characteristics described in the Player's Handbook, choose 1d4 + 1 of the following features: small horns; fangs or sharp teeth; a forked tongue; catlike eyes; six fingers on each hand; goat-like legs; cloven hoofs; a forked tail; leathery or scaly skin; red or dark blue skin; cast no shadow or reflection; exude a smell of brimstone.

It is therefore possible for a tiefling to have no horns, provided they are not of the blood of Asmodeus.

Other options

You can, of course, ask your DM if you wish to play something non-standard. This kind of minor detail of physical appearance does not affect game balance.