Most exotic mammals with a few exceptions.
Hamsters, Gerbils, Chinchillas, Guinea Pigs, Rabbits. (Unless one of these appeals to Liam as a first pet someday, of course.)
Turtles/Tortoises/Terrapins
Pigs.
Venomoid snakes, and those that grow into giants like Retics, Burms and Anacondas.
I'm sure there are others but that's all I can think of off the top of my head.