I have been looking around for different methods of attaining long term pets/companions. I am not including methods like using a spell for a short term effect like summon elemental or the like. So far these fit the intent of a permanent pet/companion that a single player can have in concurrence:

• Find Familiar (Wizard Spell-1st level)
  Find Steed/Greater Steed (Paladin Spell-2nd level/4th level)
  Homunculus (Wizard Spell-6th level)
  Steel Defender (Artificer Battle Smith Ability - 3rd)
• Beastmaster Companion (Ranger ability)
• Homunculus Servant (Artificer ability-6th)
• Mouse/rat (Urchin background best with forest gnome)
• Simulacrum (Wizard Spell-7th level)

Is there and other methods that would allow more than 4 pets/companions at a time? Granted this would be one messed up build, but I was just wondering how pet heavy a character could actually get without diving into short summon spells. Also, NO raising an infinite army of the dead, no one wants to see that walking into town and you know it necromancers! HAHA.

Animal Friendship maybe? It only lasts for 24 hours, but can be upcast to have more animal friends.

It depends on what you class as long term and what you class as a pet/companion and what rules you allow:  What about..

• Artificer Arterialist gets:
  • An Eldritch cannon at level 3
  • Can infuse a Homunculus Servent at level 6 (available to any artificer) (though there is DM interpretation if this stackable with Create Homunculous)
  • A 2nd Eldritch Cannon at level 14
• level 2 Wildfire Druid For summon Wildfire Spirit (only lasts an hour so is this short term)

Of course you can't get all of these but I think an Arterialist Artificer 14, Wizard 1, Beastmaster 3, Wild Fire Druid 2 gets you 6 if everything is an option.  It even gives the other players a chance to make a coffee while it is your turn in combat.

An Arterialist / Wizard build is perfectly playable and gets most of these.

P.S. Note on Animal friendship, a charmed animal is not controlled by you, it can not attack you or target you harmful abilities or magical effects and you have advantage on any ability check to interact socially with it (As a DM I would allow this to include an animal handling check to prevent it attacking you companions), in any case I don't think this would class asa pet.

I did look at Animal Friendship and felt it did not fit the pet role due to exactly what Jegpeg stated. The eldritch cannon only lasts for an hour like a short summon spell and it lacks the autonomy of a pet. I had never looked at the Artificer, but this looks like a lot of fun, especially the Battle Smith. The Battle Smith does get a pet, the Steel Defender which I added above. The Artificer is a pretty fun looking class.

The Urchin background grants you a pet rat. 

Go to a pet shop: 25 gold will get you a doggie, 75 for a good horse. If it's a good one, you might even find an elephant for 200!

In all seriousness, trained animals are designed to be purchased, without the need for a class feature to do so. Not every mounted horseman you encounter is a Ranger or a Paladin, war-trained animals capable of traveling with and obeying their handlers are a common resources. Heck, the Cavalier Fighter subclass is built around Mounted Combat... but doesn't have a class feature that provides a mount, it's just assumed you'll pony up (ha!) 400 gp for a Warhorse or something similar.

The animal companion of a Beast Master, the magical steed provided by Find Steed, the crafty critter provided in Find Familiar... these all have buffs and abilities that go above and beyond those of a normal member of their race. Their existence does not imply that you can't just have a Mastiff that travels with you and acts like an ally in combat, one who takes its own independent turn and makes its own decisions. There are even rules provided for how a regular store-bought Mount normally works, when you don't have a spell or class feature providing you some magical way of mind controlling it:

Controlling a Mount

While you’re mounted, you have two options. You can either control the mount or allow it to act independently. Intelligent creatures, such as dragons, act independently.

You can control a mount only if it has been trained to accept a rider. Domesticated horses, donkeys, and similar creatures are assumed to have such training. The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.

An independent mount retains its place in the initiative order. Bearing a rider puts no restrictions on the actions the mount can take, and it moves and acts as it wishes. It might flee from combat, rush to attack and devour a badly injured foe, or otherwise act against your wishes.

In either case, if the mount provokes an opportunity attack while you’re on it, the attacker can target you or the mount.

Buying an animal is an option, but lacks the special abilities a pet offers. The pet rat of the Urchin background is really cute though. If you can speak with animals, having a pet rat would be like a cute cantrip in the vein of those like prestidigitation. A forest gnome urchin for example.

A pet animal offers no inherent special abilities. A purchased dog and an urchin's pet rat are both controlled by the DM not the player, and will do what the DM decides they will do. The player controls only those companion creatures with rules which specify that control (and usually the many restrictions on it) - ranger's companions, various summoned creatures, etc.

The posts above summarise the various convoluted ways to acquire such companions, but it is worth asking the OP what the actual goal here is: are we trying to power up a team of combat animals so you are not one character in battle but 5 creatures fighting in unison? Or is this a roleplaying thing where you just want your character to be surrounded by friendly animals, but don't mind if they have no mechanical powers? 

If it is the former, then this can have a huge impact on combat encounter balancing, and as such is supposed to not be easy. If it is the latter, then just ask your DM if your character can have 5 cats which are there for RP reasons and will never contribute mechanically. Should be fine...

RegentCorreon, I was honestly just wondering how many ways there were to acquire pets similar to the find steed or find familiar spells for fun. It was more of a thought exercise over any specific character idea. Also, qualifying how the pet would be controlled and whether it could have autonomy was something that developed through these back-and-forths. The impact of walking into a player with a tiny horde of squishy annoyances might be hilarious to play, or frustrating to go against as an NPC. The Urchin rat is more of a stretch for what I was looking for, but just seemed to cute not to include it as a bonus of having a weirdly loyal animal companion right off the start.The GM would control its actions, but if you could communicate with it, maybe very small, very simple tasks could be persuaded into the GM.My main qualifications would be that the pets be under your control and not be bound to a concentration spell or limit on summoning time. You go to sleep and wake up and there they are, ready to do insane things that you imagine on a whim. Also, something you could walk into any town and not immediately be looked at like you are a freaking abomination out to raise little Timmy to join your putrid, stink parade, hence the no undead pet clause.

Then I started to see if it would be possible to make a character that could have access to all of these. I am not very good at optimization, but maybe Beastmaster 3 / Bard 13 / Battle Smith 3. Use your bard secrets to pick up Homonculus and Find Steed/Greater Steed?

I still think the Homunculus Servant should be included. There is no time limit and it has more more functionality than a familiar. While the name includes the word homunculous itis quite different from the homunculous creased by create homunculous so I do not think it should prevent create homunculous being cast due to "You can have only one homunculus at a time. If you cast this spell while your homunculus lives, the spell fails.". If it does that rises the question what would happen if the servent was infused after the spell was cast, there is no such restriction on the infusion so does it fail? Does the existing homunculous die?.

Even if a DM rules that a player can not have a  homunculous and a homunculous servent it does give an option for the player as to which he prefers

Another option is simulacrum (7th level wizard spell)

I get it now, I am unfamiliar with the Artificer, but I was reading the Infusions last night and finally understood what you were speaking about. The Similacrum spell is also viable, but I had not been thinking of them as a pet, but they completely are. You can also pull the exploit with wish to cast them in infinitum I believe, which was another reason I was excluding the Necromancer exploits. But getting up to 7th level spells is a hefty dig. Thanks for the adds Jegpeg.

There are also magic items that transform into beasts. 

Tiny Servant (3rd-level Wizard and maybe some other classes) creates an animated friend out of a small object for 8 hours.

I looked at tiny servant, but took it out because it has a time limit requiring it to be cast daily or even multiple times daily. So far I am finding a character can have the most pets (5 legit + 1 for funny) with this combination of classes:

Forest Gnome (Speak with small beasts)

Urchin Background (Receive a loyal pet rodent that you can communicate-ish with)

Bard 14: Find Familiar (Wizard Spell-1st level), Find Steed/Greater Steed (Paladin Spell-2nd level/4th level), Homunculus (Wizard Spell-6th level)

Artificer 6 [Battle Smith]: Steel Defender (Artificer Battle Smith Ability - 3rd), Homunculus Servant (Artificer ability-6th)

Here is a problem, 6th lvl spell = wizard lvl 11; 2nd lvl spell = paladin lvl 5;  artifice lvl 6.

So your best bet would actually be a Lore Bard, that can learn spells from other classes. So you look at 6lvl artificer for the infusion and 14 lvl of bard for wizard and paladin spells.

Bhuraelea, that is exactly what I have in the post just above yours. I put it in bold to make it more visually prevalent. Funny thing is, you do not have to be a Lore Bard because the extra Magical Secrets is gained to early to be used for the Homunculus (Spell level 6th). That lets you play with other kinds of Bard variations that might have some synergy with the bizarre class combo which requires a high INT and CHR. Also using at least 3 secrets for Familiar, Greater Steed, and Homunculus instead of more powerful options.

You could be riding a Peryton, with an owl familiar, homunculus, homunculus servant, and a Steel Defender in tow. Add the mouse for fun and that would be a fun NPC to run into or a very time heavy PC to have at your table. Imagine trying to commands verbally and telepathically every round, your brain would go boom.

When it comes to the base find familiar spell, don't forget that it can be acquired using either the magic initiate or ritual caster feats, so there isn't a need to spend a magical secret on a 1st level spell. That is if you don't mind giving up an ASI. The Wizard ritual caster feat probably works best for this since it would also allow you to scribe the spells Phantom steed & unseen servant, which although not permanent would still add to your total pets available if you needed them (it's also just a great utility feat in general for longer campaigns, and the available spell levels scale as a full caster would).

This means when you hit bard 10, you can select both Find Steed & Find Greater Steed together. But note, only one can be active at a time, so you may as well just pick Greater Steed & pick something more powerful for your second pick.

Similarly, if this was a build you were actually planning on playing and not a pure theory-crafting exercise, you'd get a similar level of thematically appropriate utility from the druid ritual feat for spells like speak with animals, animal messenger, beast sense & commune with nature (although no more companions here unfortunately). These would also aid you greatly if you did decide to go down the route of befriended animals, rather than ones magically bound to you buy the various class abilities mentioned.

There's probably also a bunch of other ways to get pets bound or not via items or just based on the lore of the creatures themselves. Some that come to mind are:

- Trained animals & mounts, available for purchase in some settings.
- Magical Beasts. Guard drakes are explicitly described as being created by powerful magic users with a ritual. Spectators can also be summoned this way and there are probably tonnes of others too. This is entirely dependent upon having access to the components, knowledge of the rituals etc. so are not easy, but can at least be sought out. Talk to your DM.
- Similarly to Magical Beasts, certain monsters have the "variant familiar" tag which although meant for NPC's, could potentially be acquired by PC's if your DM is nice.
- A Staff of the Python (uncommon) can be treated as a permanent giant constrictor snake you control.
- The Feather Token (Bird) (rare) Summons a multicoloured Roc which doesn't seem to disappear if it doesn't fly too far? Unsure on this one.
- A Manual of Golems (very rare) allows you to create your own Golem that is permanent and under your control, and comes in various flavours.
- Bind a Nightmare with an Infernal Tack. This is a Legendary item that binds a Nightmare to your service effectively permanently (1 action to summon for 24h, no cooldown)
- May as well throw in a sentient weapon or two for good measure

Also while we're at it, may I recommend the spells Awaken & Geas for a near limitless supply of plant / creature minions that although not *directly* under your control, are still fairly reliable for at least the first month of their service? Just make sure to make plans for when the initial charm wears off!

Quote from theHumanChris >>

Buying an animal is an option, but lacks the special abilities a pet offers.

 This is the problem. It sounds like you want to acquire a pet as a means to increase your character's overall power, not just for fluff/RP/niche utility. You ought to play a class which focuses on that aspect.

1) !!! Roleplay !!!
2) A gift/reward from an archfey. With this method, barring DM intervention, if the companion dies it is dead (barring Revitalize or similar magics).
3) For some reason unknown to the character(s), the potential companion just starts following one of the characters around.

So, so many possibilities. :)