There are Cat Face emojis #89 with some of the emotional expressions (gestures and grimaces) also offered by abstract human emoticons.

• 😸 ≈ 😁
• 😹 ≈ 😂
• 😺 ≈ 😃
• 😻 ≈ 😍
• 😼 ≈ 😏
• 😽 ≈ 😚
• 😾 ≈ 😡
• 😿 ≈ 😢
• 🙀 ≈ 😱/😩

The same feature has been requested for other animals and anthropomoprhic emojis as well. Respective sticker apps like Petmojis have been made and are being sold. The latter include the Ghost 👻, Devils 😈 👿 👹, Aliens 👽 👾 #7, Robot 🤖, Skulls 💀 ☠️, Pile of Poo 💩 and Pumpkin 🎃, but also other existing or upcoming human characters (e.g. 👶 👦 👧 👨 👩 👱 👴 👵 👲 👳 👮 👷 💂 🕵 🎅 👼 👸 👰). The former includes basically every animal, but especially mammals – most often the Dog – and the ones that are usually displayed as a head only in particular (not all of which have Face in their Unicode designation): joypixels/emojione#419

• Dromedary Camel 🐪 is shown as a camel’s head in Emojione, while the Bactrian Camel 🐫 has its full body, with 2 humps. Face of Disapproval emoji #357
• Bear 🐻, Panda 🐼, Lion 🦁, Fox 🦊, Frog 🐸, Hamster 🐹, Wolf 🐺, Unicorn 🦄 have FACE in their name and are usually displayed as heads.
• Koala 🐨, Boar 🐗, Penguin 🐧, Bird 🐦, Chick 🐤🐥 and Chicken 🐔 are sometimes shown portrait-only, by Apple in particular – and they are grouped together in their GUI for this reason.
• Unicode 9 animals Gorilla 🦍, Deer 🦌, Rhinoceros 🦏 and Eagle 🦅 do not feature FACE in their names, but are displayed as heads in several implementations, including Emojione. (The rhino is the only mammal head not facing the reader in Emojione!) Apple and Microsoft disagree. Pirate emoji proposal #339
• Some other animals, e.g. Ram 🐏, Sheep 🐑 and Goat 🐐 or Elephant 🐘 are also sometimes shown as heads. All of these are used as Asian Zodiac signs.
• It’s unclear how vendors will handle new animal emojis coming to Unicode 10 in June 2017: Giraffe 🦒, Zebra 🦓, Hedgehog 🦔, Sauropod 🦕 and T-Rex 🦖.
• Many other large animals come in explicit pairs, Dog/Poodle 🐕 🐩 / 🐶, Cat 🐈 / 🐱, Mouse/Rat 🐁 🐀 / 🐭, Rabbit/Bunny/Hare 🐇 / 🐰, Tiger/Leopard 🐅 🐆 / 🐯, Cow/Ox/Water Buffalo 🐄 🐂 🐃 / 🐮, Pig 🐖 (🐗) / 🐷 / 🐽, Monkey 🐒 / 🐵 🙈 🙉 🙊, Horse 🏇 🐎 / 🐴, Dragon 🐉 / 🐲.

Some vendors have associated certain facial expressions with particular animals, which has met with criticism. joypixels/emojione#339

It would not be feasible to encode each animal face with many different emotions. Instead, they could be the result of Emoji ZWJ Sequences: either {animal face emoji} + U+200D + {emoticon emoji} or, vice versa, {emoticon emoji} + U+200D + {animal face emoji}. Another possible option is to treat (most) existing emoticons as precomposed characters by introducing Combining Facial Expressions, e.g. for Laughing Eyes and Open Mouth.

Once introduced, both methods could also be combined. Only accessories like clothes (hats 👒 🎩 ⛑ 🎓 👑, glasses 👓 🕶, makeup 💄 💋, etc. ) and symbols (anger 💥 💢, sparkles ✨ ❇️, dizzy 💫, hearts ❤️ 💛 💚 💙 💜 🖤 💔 💕 💞 💓 💗, idea 💡, working ⚙️ ⚒, sweat 💦, tear 💧, bubbles/balloons 🗯 💬 💭 etc. ) would need to be possible right-side components then, e.g. ☺️ + 🕶 = 😎 Cool but 😑 + 🕶 = Tough. This is very similar to ordinary letters and combining diacritics in Unicode. Some diacritics also exist in an independent form (e.g. U+005E ^ and U+02C6 ˆ vs. U+0302).