And a monkey with four asses.
::from that wacky geneticist who lives on the edge of town::
We have those. They’re called house cats. 
Then feathers! A feathered boa, perhaps? sub[/sub]
Miniature Sumatran Rhinos. There would be nothing like coming home to a little hairy rhino to cheer me up after a bad day at work!
Trainable wolverines.
Oh, and one of these.
[sub]Check out The Ugly Zoo for more of the same![/sub]
Small (4-5 inch tall) gargoyles that one could train to sit on the shoulder or attack other people… with glowing red eyes of course.
Small (5 inch long) dragons with or without wings… without fire-breathing abilities. Medieval type.
Imps (generally thought of as small) that one could train like the gargoyles but also train to pick pockets on command.
I’ll be happy when they can breed housecats that don’t view Hurling as a competitive sport. I swear, mine have hurling contests sometimes. For those who want larger housecats, look into Maine Coon cats. Those babies can weigh up to 25 pounds without being fat! For comparison purposes, my normal sized cats weigh 9 and 11 pounds.
Ditto on the flying horses/poop issue.
I have worked with horses, including shoveling their byproducts.
I already have flying pets called “birds”. I have experience cleaning up their byproducts, too, come to think of it.
The idea of a pet that flies like a bird, poops like a horse… {{{shudder}}}
This thread reminds me of the story by Heinlein “Jerry Was A Man” It had the concept of genetically engineered animals, including a cute miniature elephant named Napoleon.
Ugh, I truly hope that all of these pets are litterbox trainable.
Gulo gulo, I enjoyed the pictures. Thanks for a great laugh.
Parakeets with full human intelligence.