If they are more complicated than Diamond sets forth (in his book(s) not having had his classes) doesn't that argue for less domestications?
Okay, here's some things that Diamond overlooks or underplays.
First, there's considerable support for the notion that domestication is a mutual process. A species literally self-domesticates through mutualism. ie, humans have something or produce something that a given species requires, wants or benefits from. A natural selection takes place where human habituated and human tolerant animals in a species experience a net advantage - usually more year round or specialized access to food sources.
Dogs, goats, pigs, in different ways, all found human garbage delicious and noted that when humans were around, the feeding was good.
Dogs, cats and weasels also found that where there was humans, there were lots of vermin/prey animals. The feeding was good.
Horses, Water Buffalo, Camel, Cattle were all grazers who found that humans were a species who were devoted to clearing bush, cutting down forests, and making these wonderful endless fields of delicious grazing material.
To get at the goodies, the animals have to habituate to humans. They have to be able to tolerate the presence of humans, they have to be able to monitor and distinguish humans and human behaviour to recognize when there's a threat.
Second, there has to be a viable economic reason for domestication. There's a few wrinkles there.
(i)(a) Any domestication involves time and labour, an economic expense. If you already have a domesticate doing that job, then you don't bother domesticating a second species. Existing domestications block future domestications, it's basic economics. Horses, Cattle, Water Buffalo, Yak, Camels, Reindeer, Llamas were all domesticated in different regions - and of these, only Cattle and Horses share the same niche - Water Buffalo, Yak, Reindeer and Camels all endure as economic domestications because horse and cattle don't work well. Chickens are a very dominant microlivestock, because they're so dominant, other microlivestocks like turkeys, guineau pigs, rabbit and geese are relatively marginalized.
(i)(b) Economics is also sometimes a factor in driving out or neutralizing domesticates or potential domesticates. For instance, cats pretty much pushed out domesticated ferrets, they were a more reliable verminator. There's some evidence for a Moose domestication in northern europe that did not survive economic/political competition with horse and cattle.
(ii) There actually has to be a use. Raccoons are human habituated to an extreme expense, they're tamed regularly for hundreds of years, they breed easily in captivity.... no one has ever figured out an economically useful thing for raccoons to do. Same with bears, seagulls, crows, rats, squirrels.... Pigeons sort of got borderline - there were a few economic uses (food, messengers, specialty pets, etc.)
(iii) The uses have to pass certain economic tests for cost effectiveness. Take elephants, 25 year maturation period, do the labour of a bulldozer, for elephant domestication, you really need some skewed social economics.
(iv) It's not a universal thing. Every society has different needs and requirements. The Caribou and Reindeer are genetically identical. The Sammi domesticated the Reindeer, the Inuit did not. Were the inuit stupid? No. Were the Caribou somehow unique? No. Inuit society was a transient hunter-gatherer society which moved back and forth between land and sea, domesticating Caribou would have a huge economic cost in terms of surrendering a lot of sea access and the benefits and opportunities thereof.
Three, there has to be a viable interface. Most times, animals are simply free protein. Domestication or taming is an iffy prooposition. And free protein is very very tempting. So here's the thing, if you've hunted your local populations to extinction.... no domestication possible. So there needs to be a continuing interface between human populations and wild populations in order for domestication to take place. This usually means that domestications cannot take place in the human central territories. Rather, it takes place on human borderlands. And it usually means that the potential domesticate has a refuge or place where humans find it inaccessible to replenish their population.