Under the DMG Diagonals variant (DMG 252)

• 55 attacks against ground-based Medium-sized enemies

• 175 attacks against flying Medium-sized enemies

• 181 attacks against tightly-packed, ground-based, Tiny-sized creatures

• 661 attacks against tightly-packed, flying, Tiny-sized creatures

Under the default rules for movement

• 63 attacks against ground-based Medium-sized enemies

• 263 attacks against flying Medium-sized enemies

• 213 attacks against tightly-packed, ground-based, Tiny-sized creatures

• 1013 attacks against tightly-packed, flying, Tiny-sized creatures

Constituição: Hunter Ranger 11/ Fighter 2/ Sorcerer 6

• Ranger's features: Horde Breaker, Volley

• Sorcerer's features and spells: Quickened Spell, Scorching Ray, Haste

• Lutador: Action Surge

• Talentos: War Caster, Magic Initiate (Eldritch Blast)

• Nível de Conjurador: Eleven (5 from Ranger, 6 from Sorcerer)

The Ranger is carrying all the weight here. Let's break it down.

• Açao Social: Volley. "You can use your action to make a ranged attack against any number of creatures within 10 ft of a point you can see within range." In a grid, this means you can choose a space as the center, and count two spaces from there to the up/down and left/right directions. This forms a cross that is 5 squares tall and 5 squares wide, which already contains 9 squares. If we count the diagonals as well, we can cover the tiles to the northeast, northwest, southeast, and southwest of the center square; we can also get the "Knight squares," or the ones you can reach by going two squares in one direction and one square in the perpendicular direction. There's 4 of the first and 8 of the second, adding up to 21 squares in total that is within range of your Volley. This counting rule uses the DMG Variant in DMG 252 where diagonals are measured as 10ft every other square, and 5ft otherwise; without the variant, we can cover 25 squares.

  • Nota: If you went up against packed Tiny-sized enemies, each 5ft x 5ft area can fit 4 creatures in 2 dimensions. This means a single Volley would allow 84 attacks (100 without the variant).

  • Side Note 2: If they are flying Tiny creatures and the center point was in the air, and we were able to cover a full sphere, a sphere with a 10 foot radius can contain 81 cubes, or 324 flying Tiny creatures. You can work this out by 3D symmetry: all the cubes in a larger 3x3x3 cube are in range of Volley, and 9 cubes on top of each face of the larger cube would also be in range due to the diagonal movement rule (and there are 6 faces); without the variant, we are looking at a 5x5x5 cube, for a total of 125 cubes in range. Against flying Tiny creatures, we can reach 500 of them this way.

• Quebrador de Horda: after you make your first attack, you can attack a different creature within 5 feet of the first attack's target. This is one more attack.

• Ação Surge: Use Volley a second time, adding 21 more attacks.

• Haste Action: Make one more attack.

• Ação bônus: Quickened raio abrasador at level 6. At this level, raio abrasador will make 7 attacks.

• Reação: Trigger an Opportunity Attack with War Caster and cast explosão de eldritch, adding a further 4 attacks.

Notas finais

1. You cannot replace the Sorcerer levels with a anel de armazenamento de feitiços, or else you cannot cast raio abrasador as a high level bonus action.

2. You don't need a spellcasting focus, as raio abrasador e explosão de eldritch require only VS, and not M.

GRAND TOTAL: 12 ATTACKS**

**This is based on a single class build with a standard attack scenario of enemies(or against a single BBEG/foe). The 12th attack does require some help to activate.

A 20th level Fighter-Samurai with the following abilities/buffs would get:

• Standard Attack Action: 4 Attacks
• Action Surge: 4 Attacks
• Ação bônus: 1 Attack (this could be from a variety of sources, assuming one has been chosen)
• Haste Buff: 1 Attack
• Rapid Strike: 1 Attack(would need advantage on an attack in order to exchange advantage for 2 attacks)
• Reaction: 1 Attack (Would need to set this up with another party member)

Examples of Bonus attack sources

Ações de bônus

• Empunhadura dupla
• Grande Mestre em Armas
• Mestre de arma de fogo

Reactions (pick one!)

• Opportunity Attack provided by another character holding a Readied Action to cast Dissonant Whispers on your turn when you attack.
• An attack could also be provided by a Battlemaster Fighter using Commander's Strike.

Infinity.

As always with this sort of question, it's difficult, but there's no limit to the number of attacks you can make in a single turn. Use Shapechange or Polimorfo verdadeiro to turn into...a hydra! The hydra's multiattack works like this:

Multiattack. The hydra makes as many bite attacks as it has heads.

And its heads work like this:

Whenever the hydra takes 25 or more damage in a single turn, one of its heads dies. If all its heads die, the hydra dies.

At the end of its turn, it grows two heads for each of its heads that died since its last turn, unless it has taken fire damage since its last turn. The hydra regains 10 hit points for each head regrown in this way.

So just find some way to kill heads over and over again, as well as some way to heal yourself so you don't die from your HP total reaching 0, and your number of attacks will be limited only by the time it takes you to grow more heads.

Grand total, 17 Attacks

This answer assumes that you are hoping be able to use this tactic against a single enemy, using a character that has the form of a playable race, and that you want all of your attacks to be able to add your Ability modifier to damage.

Full credit to NautArch, whose answer I've already upvoted, as mine is similar to his.

I'm pretty sure you meant "weapon attacks" when you said "attacks". But if you meant spell attacks, then a Sorcerer/ Warlock/ Fighter build will give you some options. Consider the following:

Level 20 character, with 2 levels in Warlock (for Eldritch Blast and the Agonizing Blast invocation), 2 levels in Fighter, and the remaining levels in Sorcerer. The build will also require the War Caster Feat, and would benefit greatly from the Crossbow Expert Feat. Every casting of Eldritch blast at level 17 or higher allows you to make 4 separate attacks. This will result in:

• Standard Action: Eldritch Blast 4 attacks
• Bonus Action: Quickened Eldritch Blast 4 attacks
• Action Surge: Eldritch Blast 4 attacks
• Haste Action: Draw and throw knife: Ataque 1
• Reaction: War Caster - Eldritch Blast as Opportunity Attack 4 attacks

This adds up to a total of 17 attacks once per combat (Action Surge only once in this build), or 13 attacks on other rounds. Of course, the Opportunity Attack will be hard to set up (See Resposta de NautArch for how this could be done), and all 4 of those Reaction attacks would need to target only the creature that triggered the attack. Still, Quickened Eldritch Blast is notable in allowing a character to turn a bonus action into the equivalent of a full action Extra Attack.

Crossbow Expert will not give you any extra attacks in this system. But it is quite important, because if you are gaining an Opportunity Attack in this scenario, then an enemy is likely within 5 feet of you for a lot of these attacks. Crossbow Expert will keep you from having to make most (if not all) of these attacks with disadvantage.

Small side note: if you desperately wanted all 17 attacks to be made with your best attack attribute (20 Charisma), then you could go for Warlock 3, Fighter 2, Sorcerer 15 (rest of the build unchanged), and Variant Human race to get the Crossbow Expert Feat. This would allow you to gain Shillelagh as a Warlock spell through the Warlock Invocation "Book of Ancient Secrets". You could use a staff as a focus for casting, and having cast Shillelagh on a previous round, could use your Haste attack to make a melee attack with the staff, using Cha as your attacking ability.

21 attacks

This is self-sufficient and you are still the one making the attacks, unlike in @Voromier Kadien's answer. It also doesn't require enemies to be conveniently clumped up as in Resposta de @ user27327.

Build: Fighter 2, Sorcerer 17, Monk 1. Editar Removed Warlock 1, as a Acelerado cantrip precludes the use of non-cantrip spells that turn.

Pre-combat: Pressa, self-cast.

Ação: Raio Escaldante cast at level 9, giving you 10 attacks (3 base + 1/level above 2).

Action Surge: Raio Escaldante cast at level 8, giving you 9 attacks.

Pressa action: 1 attack with unarmed or monk weapon.

Bonus Action: Unarmed attack given by Artes marciais Monk ability.

If an enemy leaves a threatened space, you can also spend your Reaction to make an unarmed attack again for an additional attack (bringing the total up to 22). However, this isn't under your control, so I didn't add it to the calculation.

Bonus points if you have a spellcasting ally or Bracers of Haste to cast Haste on you, thus freeing you up to Hex the target beforehand. Might as well take advantage of all those attacks and dish out an extra 21d6 damage ;).

I'm not sure if this is the absolute highest possible, but a 20th level dual wielding Fighter using Action Surge can make 9.

Using the Attack action is 4, using Action Surge for another Attack is another 4, and your bonus action for an off-hand attack.

Truly infinite, but only if: Tunnel Fighter (UA: Light, Dark, Underdark!) Fighting Style and Feats are allowed for your campaign.

Combine it with Sentinel feat, a polearm, and Polearm Master feats. The result is that properly positioned the character can hold off a horde of enemies and have opportunity attacks against them all, all the time instead of just once per turn. Whenever they come into your reach or try to leave it. Best corridor warden, preferably in full plate.

Technically, 39 attacks

The Build

Fighter 2 / Bard 17 who learned raio abrasador, aljava rápida e contingência via the Magical Secrets feature and has War Caster.

O Setup

Somehow acquire two 9th level raio abrasador scrolls and a Potion of Speed.

Elenco contingência com um nível 5th raio abrasador and the condition "when I expend my 9th level spellslot". Yes, the rays will target me, but the attacks still technically take place.

Elenco aljava rápida, quaff the Potion of Speed, and end my turn while holding one of the scrolls and a bow.

A vez

• Action, 10 attacks: read the 9th level raio abrasador scroll.
• Action Surge, 10 attacks: take out and read the other 9th level raio abrasador scroll.
• Hasted Action, 1 attack: take the Attack action to attack with the bow once.
• Bonus Action, 2 attacks: utilize the aljava rápida buff to attack with the bow twice.
• Reaction, 10 attacks: utilize War Caster to cast a 9th level raio abrasador instead of making an opportunity attack.
• Contingency, 6 attacks: blast myself with the effect of a 5th level scorcing ray.

Realistically, 23 attacks

In a realistic scenario, I wouldn't want to to squander my gold on consumables, I wouldn't want to blast myself, and no opponent would trigger an attack of opportunity during my own turn, hence:

The Build

Fighter 2 / Bard 17 who learned raio abrasador, pressa, aljava rápidae contingência via the Magical Secrets feature.

O Setup

Acquire the boon of High Magic.

Elenco contingência com pressa and the condition "when I intentionally loose concentration on aljava rápida".

Elenco aljava rápida.

A vez

• Action, 10 attacks: cast a 9th level raio abrasador.
• Action Surge, 10 attacks: cast another 9th level raio abrasador via the boon of High Magic.
• Bonus action, 2 attacks: utilize the aljava rápida buff to attack with a bow twice.
• Contingência: intentionally loose concentration on aljava rápida to trigger the effects of pressa.
• Hasted Action, 1 attack: take the Attack action to attack with a bow once.

4924

Construir

A bugbear ranger 11/fighter 2 with a bow and a glaive as well as the polearm master feat and the tunnel fighter fighting style.

Ranger 11 - volley:

You can make a weapon attack against every creature within 10 feet of a point you can see.

This covers 9×9×9 tiny flying creatures =729 attacks.

Tunnel Fighter

While in your defensive stance, you can make opportunity attacks without using your reaction.

Mestre de arma de fogo

While you are wielding a glaive, halberd, pike, quarterstaff, or spear, other creatures provoke an opportunity attack from you when they enter your reach.

Your reach is 15 feet (+5 from bugbear, +5 from glaive) which covers 14×14×14-8 tiny flying creatures = 2736 opportunity attacks.

Ação Surge You can take 2 actions on the same turn

Quebrador de Horda Once on each of your turns when you make a weapon attack, you can make another attack with the same weapon against a different creature that is within 5 feet of the original target.

Cenário

You are flying and about to be surrounded on all sides by a horde of tiny flying creatures.

You then ready a volley (729) for when one of them gets too close.

You also have the tunnel fighter fighting style and use your bonus action to enter a defensive stance.

After firing you volley they all sound you triggering the 2736 opportunity attacks.

Now your turn begins, you take the volley action, then you take it again with action surge. That's another 729*2=1458 attacks.

Total

Reaction volley - 729
Opportunity attacks - 2736
Action volley - 729
Action surge volley - 729
Horde Breaker - 1
= 4924

25 Attacks

Fighter 20 (samurai)

If the situation is there, you need a way to gain haste and be dual wielding, then you have the ability to forgo advantage and add one additional attack as part of your attack action once per turn. After that use Action Surge to gain 5 more attacks. If on that same round you are knocked down to zero HP, you instantly gain another turn (not an action, but a full turn) which you repeat the same turn previously taken. Finally you need a way to use your reaction in that round.