Did Darwin explain why he believed that domestic dogs descend from several distinct species of ancestor?
"Does (Darwin) explain elsewhere his detailed reasons for his conclusion?"

Yes. After Origin of the Species, he wrote a whole book, The Variation of Animals and Plants under Domestication (1868), which begins with Chapter 1.I on "Domestic Dogs and Cats".

He writes that "we shall probably never be able to ascertain their origin with certainty" and then gives detailed sources for both sides of the argument. It's Pallas against De Blainville.


  Firstly, the great difference between the several breeds; but this
  will appear of comparatively little weight, after we shall have seen
  how great are the differences between the several races of various
  domesticated animals which certainly have descended from a single
  parent-form. Secondly, the more important fact, that, at the most
  anciently known historical periods, several breeds of the dog existed,
  very unlike each other, and closely resembling or identical with
  breeds still alive (...)
  
  (A)t a period between four and five thousand years
  ago, various breeds, viz. pariah dogs, greyhounds, common hounds,
  mastiffs, house-dogs, lapdogs, and turnspits, existed, more or less
  closely resembling our present breeds (...)
  
  As long as man was believed to have existed on this earth only about
  6000 years, this fact of the great diversity of the breeds at so early
  a period was an argument of much weight that they had proceeded from
  several wild sources, for there would not have been sufficient time
  for their divergence and modification. But now that we know, from the
  discovery of flint tools embedded with the remains of extinct animals
  in districts which have since undergone great geographical changes,
  that man has existed for an incomparably longer period, and bearing in
  mind that the most barbarous nations possess domestic dogs, the
  argument from insufficient time falls away greatly in value (...)
  
  The existence of a single race, remarkably constant in form during the
  whole Neolithic period, is an interesting fact in contrast with what
  we see of the changes which the races underwent during the period of
  the successive Egyptian monuments, and in contrast with our existing
  dogs. The character of this animal during the Neolithic period, as
  given by Rutimeyer, supports De Blainville's view that our varieties
  have descended from an unknown and extinct form.


At this point it's not looking good for Pallas. But Darwin continues:


  (W)e should not forget that we know nothing with respect to the
  antiquity of man in the warmer parts of the world. The succession of
  the different kinds of dogs in Switzerland and Denmark is thought to
  be due to the immigration of conquering tribes bringing with them
  their dogs; and this view accords with the belief that different wild
  canine animals were domesticated in different regions (...)
  
  The main argument in favour of the several breeds of the dog being the
  descendants of distinct wild stocks, is their resemblance in various
  countries to distinct species still existing there.


Moreover,


  (s)everal canine species evince no strong repugnance or
  inability to breed under confinement; and the incapacity to breed
  under confinement is one of the commonest bars to domestication.
  Lastly, savages set the highest value (...) on dogs: even half-tamed
  animals are highly useful to
  them: the Indians of North America cross their half-wild dogs with
  wolves, and thus render them even wilder than before, but bolder: the
  savages of Guiana catch and partially tame and use the whelps of two
  wild species of Canis, as do the savages of Australia those of the
  wild Dingo. Mr. Philip King informs me that he once trained a wild
  Dingo puppy to drive cattle, and found it very useful. From these
  several considerations we see that there is no difficulty in believing
  that man might have domesticated various canine species in different
  countries. It would indeed have been a strange fact if one species
  alone had been domesticated throughout the world (...)
  
  If any wild canine species had distinctly exhibited the tan-coloured
  spots over the eyes, it might have been argued that this was the
  parent-form of nearly all our domestic races. But after looking at
  many coloured plates, and through the whole collection of skins in the
  British Museum, I can find no species thus marked. It is no doubt
  possible that some extinct species was thus coloured (...)
  
  The belief that our dogs are descended from wolves, jackals, South
  American Canidae, and other species, suggests a far more important
  difficulty. These animals in their undomesticated state, judging from
  a widely-spread analogy, would have been in some degree sterile if
  intercrossed; and such sterility will be admitted as almost certain by
  all those who believe that the lessened fertility of crossed forms is
  an infallible criterion of specific distinctness. Anyhow these animals
  keep distinct in the countries which they inhabit in common. On the
  other hand, all domestic dogs, which are here supposed to be descended
  from several distinct species, are, as far as is known, mutually
  fertile together (...)
  
  Pallas assumes (...) that a long course of domestication eliminates that
  sterility which the parent-species would have exhibited if only lately
  captured; no distinct facts are recorded in support of this
  hypothesis; but the evidence seems to me so strong (independently of
  the evidence derived from other domesticated animals) in favour of our
  domestic dogs having descended from several wild stocks, that I am
  inclined to admit the truth of this hypothesis.
  
  There is another and closely allied difficulty consequent on the
  doctrine of the descent of our domestic dogs from several wild
  species, namely, that they do not seem to be perfectly fertile with
  their supposed parents. But the experiment has not been quite fairly
  tried; the Hungarian dog, for instance, which in external appearance
  so closely resembles the European wolf, ought to be crossed with this
  wolf: and the pariah dogs of India with Indian wolves and jackals; and
  so in other cases. That the sterility is very slight between certain
  dogs and wolves and other Canidae is shown by savages taking the
  trouble to cross them.


Concluding:


  Notwithstanding the difficulties in regard to fertility given in the
  last two paragraphs, when we reflect on the inherent improbability of
  man having domesticated throughout the world one single species alone
  of so widely distributed, so easily tamed, and so useful a group as
  the Canidae; when we reflect on the extreme antiquity of the different
  breeds; and especially when we reflect on the close similarity, both
  in external structure and habits, between the domestic dogs of various
  countries and the wild species still inhabiting these same countries,
  the balance of evidence is strongly in favour of the multiple origin
  of our dogs.


In short the main support for multispecific origin is that different breeds of the domestic dog, differing from each other in many physical respects, are very ancient and they are similar to wild species in the same geographical areas.