Darwin's original suggestion was that complication and perfection could be arrived at through a great many small steps. He pointed out that a far-future payoff cannot cause a long, slow sequence of events. Each individual step has to deliver a short term benefit, and the size of a step should control the size of its benefit. And, the step must be heritable.
The benefit must be such that its possessor is more likely to leave descendants. If this is true, then each little change is statistically likely to spread throughout a population, until all the creatures in the population have it. It doesn't matter who took the step (except to him or her), since in the long term everyone benefits. The stage is then set for the next step. That next step can originate in anyone, since everyone has inherited the last step.
If we can identify a sequence that is like this, then we have found a Darwinian scenario. Of course, the fact that one scenario exists doesn't mean that it's the only possible scenario. And a scenario isn't a proof.
The eye is the classical example where we have a long, slow sequence that provides incremental benefits.
Mimicry has the same property, so it is not surprising that there are many mimics.
There are three categories of benefit. First, a step might help a creature to be competitive against others of its species. In that case, once everyone has the step, it ceases to be an advantage. The next step (if and when it arrives) is again compelling.
(For example, trees are tall, because that way they get more sunlight than the tree beside them. Except now they're all tall.)
The second category is when a step helps a creature to be competitive against some other species. Unfortunately, the other species - whether predator or prey - is then under increased pressure. The result may be an arms race.
(For example, cheetah are very good at chasing gazelles. And, gazelles are very good at running away.)
The third category is when a step just makes a creature better against raw nature. For example, a bird which flies better can travel over a larger desert. This is the sort of thing which spread birds around the world, and which brought fish (and plants and insects and fungus and bacteria) up from the seas to the land.
Any useful effect is liable to involve several interacting factors. For example, mimicry often involves changes in both color and shape. A species which becomes much larger will need changes in the bones, and eventually even in the placement of the muscle-to-bone attachments. Even worse, an arms race involves two different species.
So, these scenarios can involve an ensemble of factors. Any one of those factors could involve complex interactions at the genetic level. It's legitimate to think that the genotype involved is sometimes complicated.
This is not a problem, because we stated up front that we were talking about inheritable changes. Mathematics (and lab experiments and computer simulations) show that a complicated genotype just has a lower heritability value. The only effect is that the scenario will operate more slowly.
Actual measurements of heritability show that the slowdown is not extreme. After all, each dog breed is defined by an ensemble of features, and most of the breeds are less than 200 years old. Clearly, the heritability of those features is pretty high.