Witches again as an example.
Witches would now be neutral mobs who only attack you if you attack them, or if you destroy any of the blocks in their hut/take anything from their hut. They are given more combat ability, but they do not respawn if you kill them (no more mob farming them, sorry mate).
Witches are now required to learn new types of potions, which require that you bring them materials (sometimes related to the potion you want to make, sometimes not, a bit of randomness is the spice of randomness spice) in exchange for giving you the recipe to be able to craft said potion.
Witches also allow you to buy enchantment books (again, randomized, but higher grade is likely better, and perhaps scale it depending on how much trading you've done with the specific witch in question) for the cost of the XP to use that enchantment as well as a bit more, and likely also something expensive enough the awesomeness of getting past the horrible vanilla crafting system.
Finally, witches have a strange fascination with cats, and as such they will treat a player that has a cat following them differently/stop being aggro against said player/etc. They will also offer to trade for a black cat for whatever they would be trading for if you have a black cat following you.
Despite one wolf lasting for many episodes they still aren't that super.
Wolves are now the base genetic structure of the entire dog system. Wolves will have a few genetic values, such as size, color, aggressiveness, vitality, etc, which will be used as the wolf ages. When a player captures a wolf using either kindness (feeding it raw meat) trickery (making a small box that it cannot escape from), or cruelty (hurting it until it gives up), the wolf is given a boost to its submissive value (decent random range). This value defines how close to being wild a wolf is, and how likely it is to revert to fully wild. This value can be increased through kindness of cruelty, but each action type also increases and decreases other aspects of the wolf's genetics.
Generations of wolves end up mixing different genetic aspects to give you a wide range of sizes, colors, shapes, aggressiveness, and the like, although most values need to be careful adjusted and then carefully bred for the goal. If you're just aiming to make a duplicate of your offline pet, it's less of an issue as you likely don't care how it acts, but all functionality of dogs carry over to the form the dog takes partially.
The translation of wolf to dog is not a defined process, and ANY dog can revert to being fully wild (feral) given enough reason to do as much (abuse, starvation, etc).
Intelligence allows you to train your dog to do some tasks, such as the obvious tricks of rolling over, playing dead, and whatnot, but also fetching you something, digging (dogquarry), hunting, and the like.
Larger dogs, and more vitality-infused dogs can also be given packs to carry things.
Cats have a slight bit more use but having a well lit area provide the same function.
Cats have a similar genetic structure to dogs, and have similar abilities to do useful tasks such as sit on something and watch you, ignore you, and ignore you whilst sitting on something watching you.
You can also raise cats to trade with witches if you want an annoyingly fuzzy trading medium. Otherwise, cats aren't getting any more useful.
Also, if you're smart enough to ignore the cat side of things, you can train wild cats to become more aggressive and more interesting, until you get yourself some tigers/lions/etc oh my. Much more interesting!
And there we go, some fairly simple directions that make witches/dogs/cats mildly interesting.