This is a question I've been pondering on and off since 5e dropped. Just never gotten around to asking it before but with the sidekick rules from TCoE I figured I'd finally get around to it.
First some caveats to any answers. For it to count as a "permanent" pet it must adhere to the following criteria.
1. The pet must be based on a rule mechanical effect from the RAW. It can be a spell, a feat, a class feature or some other rule from any and all of the official books published by WotC. So no having a character buy up every kitten in Waterdeep. Likewise, mounts acquired through the equipment lists does not count nor does pets acquired through taming using skills.
2. To count as a pet the pet must be a creature from the official books.
3. To count as permanent the pet must be able to exist and stay with the character for at least one day at a time. If the pet has been summoned then the duration of the summon must be longer than the time it takes to refresh whatever resource or ability it took to summon the pet. (A so called permaspawn.)
4. The pet's existence can not be dependent on the character's concentration.
5. If the pet's existence is dependent on a rule that normally require a DM's approval consider it given for the sake of this question.
6. The character does not have to be a good or even viable build as long as it is a legal build based on the RAW. (It does matter how MAD, multiclassed or overfeated it is, just the number of legal pets it can have. )
The simplest answer gives you three pets using a Beastmaster Ranger with the Magic initiate feat for the Find Familiar spell and a sidekick from TCoE.
I think a high level necromancer could technically have mostly unlimited minions. 15th level or higher means they can cast Finger of Death as many times as there are commoners to kill, or cast Create Magen infinitely without worrying about losing hit points each time (as per 10th level inured to death). Both those require a steady stream of humanoids or gold though, so up to you if that counts.
JoJo is correct - a necromancer can have infinite pets. So can anyone with access to both wish and simulacrum; genielocks can do it with nothing but wish. An artificer can, given time, produce infinite awakened shrubs via infusing pot of awakening, and the shrubs will have no reason to stop being your friends when the charm wears off unless you piss them off. I'm assuming you don't want to count found magic items for this.
Due to the wording of your constraints, though, this is much easier - mass suggestion qualifies in spades, since you can "spam" it relative to its duration, basically guaranteeing your pets stay your pets. This also gives you nearly infinite pets by itself - the L9 version alone can be recast every day, cycling through your pets so each one is hit once per month, effectively guaranteeing they don't make it a year and a day without failing. That alone would be roughly 12/day*30 days/month = 360 pets, and if your pets can make their own pets, that explodes out your pet count.
The simplest answer gives you three pets using a Beastmaster Ranger with the Magic initiate feat for the Find Familiar spell and a sidekick from TCoE.
Anyone that can top it?
The sidekicks from TCoE are not pets. They are a mechanism the DM can use to add an NPC to the party and easily level that NPC up to keep its power level matched to the players. Nothing about it gives control of that NPC to a player by default. The creature can still be DM controlled, controlled by a player in addition to their character, or used as a simple version of a player's only character. It is definitely not a pet supplied by any rule feature a played can access like a learning a spell or feat or leveling up in a chosen class.
For most pets outside of the infinite magic shenanigans you will be looking at things like Ranger 3 Beast Master for an animal, Artificer 2 for Homunculus Servant and Artificer 3 Battle Smith for a Steel Defender, the spells 1 Find Familiar, 2 Find Steed or 4 Find Greater Steed (mutually exclusive), and 6 Create Homunculus. A Bard 14 should be able to get all those spells (College of Lore gets some slightly faster).
So Artificer 3 / Ranger 3 / Bard 14 should be able to wander around with a wolf, an owl, two homunculi, a griffon and a robot dinosaur. Leveling up in the above class order gives you new pets at levels 2, 3, 6, 12, 16 and 20. Terrible character though...
This is a question I've been pondering on and off since 5e dropped. Just never gotten around to asking it before but with the sidekick rules from TCoE I figured I'd finally get around to it.
First some caveats to any answers. For it to count as a "permanent" pet it must adhere to the following criteria.
1. The pet must be based on a rule mechanical effect from the RAW. It can be a spell, a feat, a class feature or some other rule from any and all of the official books published by WotC. So no having a character buy up every kitten in Waterdeep. Likewise, mounts acquired through the equipment lists does not count nor does pets acquired through taming using skills.
2. To count as a pet the pet must be a creature from the official books.
3. To count as permanent the pet must be able to exist and stay with the character for at least one day at a time. If the pet has been summoned then the duration of the summon must be longer than the time it takes to refresh whatever resource or ability it took to summon the pet. (A so called permaspawn.)
4. The pet's existence can not be dependent on the character's concentration.
5. If the pet's existence is dependent on a rule that normally require a DM's approval consider it given for the sake of this question.
6. The character does not have to be a good or even viable build as long as it is a legal build based on the RAW. (It does matter how MAD, multiclassed or overfeated it is, just the number of legal pets it can have. )
The simplest answer gives you three pets using a Beastmaster Ranger with the Magic initiate feat for the Find Familiar spell and a sidekick from TCoE.
Anyone that can top it?
I think a high level necromancer could technically have mostly unlimited minions. 15th level or higher means they can cast Finger of Death as many times as there are commoners to kill, or cast Create Magen infinitely without worrying about losing hit points each time (as per 10th level inured to death). Both those require a steady stream of humanoids or gold though, so up to you if that counts.
JoJo is correct - a necromancer can have infinite pets. So can anyone with access to both wish and simulacrum; genielocks can do it with nothing but wish. An artificer can, given time, produce infinite awakened shrubs via infusing pot of awakening, and the shrubs will have no reason to stop being your friends when the charm wears off unless you piss them off. I'm assuming you don't want to count found magic items for this.
Due to the wording of your constraints, though, this is much easier - mass suggestion qualifies in spades, since you can "spam" it relative to its duration, basically guaranteeing your pets stay your pets. This also gives you nearly infinite pets by itself - the L9 version alone can be recast every day, cycling through your pets so each one is hit once per month, effectively guaranteeing they don't make it a year and a day without failing. That alone would be roughly 12/day*30 days/month = 360 pets, and if your pets can make their own pets, that explodes out your pet count.
With shenanigans: infinity.
Without shenanigans: depends on class, but like 1-3.
Necromancers can still make a sizable hoard with just animate dead and no shenanigans.
Steel defender is permanent, isn’t it?
∞
The sidekicks from TCoE are not pets. They are a mechanism the DM can use to add an NPC to the party and easily level that NPC up to keep its power level matched to the players. Nothing about it gives control of that NPC to a player by default. The creature can still be DM controlled, controlled by a player in addition to their character, or used as a simple version of a player's only character. It is definitely not a pet supplied by any rule feature a played can access like a learning a spell or feat or leveling up in a chosen class.
For most pets outside of the infinite magic shenanigans you will be looking at things like Ranger 3 Beast Master for an animal, Artificer 2 for Homunculus Servant and Artificer 3 Battle Smith for a Steel Defender, the spells 1 Find Familiar, 2 Find Steed or 4 Find Greater Steed (mutually exclusive), and 6 Create Homunculus. A Bard 14 should be able to get all those spells (College of Lore gets some slightly faster).
So Artificer 3 / Ranger 3 / Bard 14 should be able to wander around with a wolf, an owl, two homunculi, a griffon and a robot dinosaur. Leveling up in the above class order gives you new pets at levels 2, 3, 6, 12, 16 and 20. Terrible character though...
You can cast Awaken two times per day and then take a long rest. The creatures are charmed by you for 30 days, so that's 60 at least.