Can a Familiar level up with its master during their adventures and improve their stats, abilities and skills, or are they fated to stay as written in the Monster Manual?
I want to know because I'm looking at a sprite for a Warlock build, and it has only 2 HP. I know I can always recast but aesthetically I kinda want it to be like a an adventuring companion. With 2 HP a falling book would kill it.
Familiars, Rules as Written, don't advance. The Pact of Chain Familiar doesn't improve stats over time. The only text we have on them is in Find Familiar and in the Pact of Chain class feature.
You learn the find familiar spell and can cast it as a ritual. The spell doesn't count against your number of spells known.
When you cast the spell, you can choose one of the normal forms for your familiar or one of the following special forms: imp, pseudodragon, quasit, or sprite. Additionally, when you take the Attack action, you can forgo one of your own attacks
You gain the service of a familiar, a spirit that takes an animal form you choose: bat, cat, crab, frog (toad), hawk. lizard, octopus, owl, poisonous snake, fish (quipper), rat, raven, sea horse, spider, or weasel. Appearing in an unoccupied space within range, the familiar has the statistics of the chosen form, though it is a celestial, fey or fiend (your choice) instead of a beast.
Your familiar acts independently of you, but it always obeys your commands. In combat, it rolls its own initiative and acts on its own turn. A familiar can’t attack, but it can take other actions as normal.
When the familiar drops to 0 hit points, it disappears, leaving behind no physical form. It reappears after you cast this spell again.
While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar’s eyes and hear what it hears until the start of your next turn, gaining the benefits of any special senses that the familiar has. During this time, you are deaf and blind with regard to your own senses.
As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits you summons. Alternatively, you can dismiss it forever. As an action while it is temporarily dismissed, you can cause it to reappear in any unoccupied space within 30 feet of you.
You can’t have more than one familiar at a time. If you cast this spell while you already have a familiar, you instead cause it to adopt a new form. Choose one of the forms from the above list. Your familiar transforms into the chosen creature.
Finally, when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell. Your familiar must be within 100 feet of you, and it must use its reaction to deliver the spell when you cast it. If the spell requires an attack roll, you use your attack modifier for the roll.
A sprite is powerful in stealth, has poison arrows, and great for flavor in a feylock. Unfortunately, it isn't very hearty. You can improve its armor (and weapons), or give it with temporary health points by magical means. The sprite familiar takes its existing equipment with it when sent to the pocket dimension, so in theory, the upgraded equipment should work go as well (there is a question on this, but even if the sprite couldn't take them with them, they are light and you can carry it). Magic items meant for PCs (isn't true of some of the weapons monsters carry) resize to the size of user, so there is no reason it couldn't use magic weapons/armor.
Any more than this would require you get your DM agree to house rule for progression.
J. A. Streich has already covered the rules well enough in his answer so I wont retread over that ground.
You say in your question:
I know I can always recast but esthetically (sic) I kinda want it to be like a an adventuring companion. With 2 HP a falling book would kill it.
Why can't it still be your adventuring companion? When you re-cast find familiar, what is preventing you from summoning the same spirit you had previously summoned into the sprite form, so that it retains its memories of its former "life"? There is nothing in the rules saying that you must summon a familiar with a new spirit, and if you're a Pact of the Chain warlock it only makes to summon the same spirit again (even if it might be in a different form).
There is roleplay value in the familiar being so weak and easily defeated. Imagine your sprite getting squashed and coming back with an earful for you when you re-summon him later at camp. Since your familiar is (presumably) bonded to you via Pact of the Chain, he may begin to resent your actions, especially if you keep getting him killed or otherwise putting him in harm's way.
I've been toying with this same idea recently. In the DMG there are optional rules for leveling NPC adventurers and for giving monsters class levels. (They function very similarly to cohorts from 3.5e, if you are familiar with that edition). You might have a hard time selling it to your DM, but you could work out with the DM a way to give your familiar class levels.
RAW for find familiar doesn't explicitly indicate the familiar can't improve. If it dies, the text can be read as implying that you resummon the same spirit. If that's how your DM handles this, then the above optional rules provide an opening to make this work for your familiar.
Monster NPCs/NPC Statistics and Using Classes and Levels - Dungeon Master's Guide pg. 92 Adventurer NPCs - Dungeon Master's Guide pg. 93
The spell find familiar does not offer any scaling.
As a Warlock you may choose the Voice of the Chain Master Invocation (PHB p.111), which does not improve the stats of your familiar but adds more usefulness.
One thing easily overlooked are magic items. Per RAW definition your familiar (a creature) should be able to attune to and use some magic items.
Ask your DM if he is OK with that; I can easily see many DMs not allowing it.
Keep in mind that some limits would be:
Maybe the DM allows you to use a homebrewed a Feat, Invocation or Magic Item to keep your familiar useful.
This is a bit of a frame challenge for your question. You say that the reason you are looking to enhance the durability of your familiar (with rules mechanics) is that you want it to be a companion, the same companion that does not die:
I can always recast but aesthetically I kinda want it to be like a an adventuring companion. With 2 HP a falling book would kill it.
And the thing is, damage will not kill it. The spell Find Familiar says:
When the familiar drops to 0 hit points, it disappears, leaving behind no physical form. It reappears after you cast this spell again
That means, when you recast the spell, the same familiar reappears from whereever it dissappeared to. It did not die. It's the same spririt. You can totally have your adventuring companion, no enhancement required. Sometimes it needs a little help to get back out of its hidey-hole.
My wizard has named his familiar, and while it has been shunted away a couple of times, it is still the same old trusty little guy, reappering in various guises.
https://www.dndbeyond.com/sources/tcoe/dungeon-masters-tools#Sidekicks
This is probably your best bet for advancing a familiar. Talk to your DM, though.
Beyond that, there are not many options in 5e.
However, this has been done in previous editions. So there is precedent out there.
If you were to go this route, you would need to check with your DM, of course. So I mention previous editions because it is a great source for ideas on how to do this. In the past this was done through:
Improved familiar stands out as probably the likeliest candidate for updating to 5e.
I will research my old docs to see if I can source these methods, but it might take some time. If / When I find them, I'll post them here.
Here is one of my favorite articles on improving familiars from Dragon #181 pg 22. While it is for 2nd Ed, it is easily translatable to 5th, and it seems like a very reasonable place to start when building familiar improvements.
There are some neat familiar feats here Dragon # 374 pg 32 - but they are from 4th Ed and would take some more work to get them into shape.
There are rules in the DMG pg 283 for giving class levels to a monster but the lead designer for DND classes on the Giant Soul sorcerer dragon+ episode at about 58:09 says there are no prerequisites for taking a class but doing it to a fimilar or the rangers beastmaster pet is not advised. Just find an animal and get some experience with. The rules are there for a reason, at the DMs mercy of course. But the DM can't say "it's not legal", because it is. You can have a wolf wizard. Let that sink in.
