Dogs and cats and some other species as well can conceive puppies and kittens sired by more than one male per litter. A dual-sired litter is a litter where two sires, instead of one, are bred to.
The dual-sired litters I am talking about here are PLANNED. They are not accidents.
While dual-sired litters are planned less frequently than single-sired litters, they are just as accepted by breed registries. While breed registries typically require DNA testing to prove parentage for dual-sired litters, parentage can sometimes be obvious from traits such as coat pattern or color.
Breeders use the same careful stud selection and screening processes for planned dual-sired litters as they do for litters with a single sire.
Pros and Cons of Dual-Sired litters
There are quite a few advantages to dual-sired litters.
Producing puppies from two sires in a single breeding can allow a breeder to produce puppies with potentially different characteristics in a single litter.
If a breeder has an unproven male or one with questionable fertility, they can use a second proven sire as a “backup” to increase the chances of conception
Using two sires for a single litter allows a breeder to evaluate the quality of a sire’s puppies in a side-by-side comparison
A dual-sired litter can add to the genetic diversity in a breeder’s program
The main downsides for a breeder can include increased breeding costs, cost of DNA parentage testing, and additional vet costs.
Who’s Your Daddy?
As with many other topics in the breeding world, there are lots of interesting opinions about whether one sire or the other or both will produce the puppies. And there are even more interesting suggestions on how to get a litter with puppies sired by both studs.
There aren’t a large number of studies on this, but there are a few, so let’s take a look at what we know and maybe put a dent in some of the “interesting” pieces of breeding advice out there.
First, anecdotally, most breeders I’ve spoken to have found that puppies tend to come from only one sire. That has been my experience as well.
A 2023 very small study in Croatia compared inseminations in two bitches during their breeding careers. One was inseminated surgically, the other transcervically (TCI). Semen from two studs was mixed prior to all inseminations. There were a total of 3 breedings completed, and only one of the three produced a litter from both sires. The other two litters were fathered by a single sire. 
A 2020 study had a better sample size, with data collected from 28 individual bitches from 10 different breeds over a 10-year period for a total of 29 dual-sired breedings.  For this study, the insemination from stud A was an AI from frozen semen from the “genetically desired” stud and always performed first; the second (and sometimes third) was either fresh or frozen AI or a live cover from stud B. Controls of 16 single-sired litters were used in the study. Progesterone testing was performed to ensure proper timing of all breedings.
Of the 29 dual-sired breedings, 26 litters were produced. Eight litters, or 30.8 percent, were determined to be sired by more than one sire, which is statistically in line with the smaller 2023 Croatian study.
In the dual-sired litters, half were produced by the first sire, and half by the second. There was no difference in average litter size between single- and dual-sired litters for each bitch. While there were no differences in litter size, conception rate was increased in bitches that had dual sirings.
In the litters where puppies came from only one sire, more were produced by the second sire than the first, with 27 percent coming from the first sire and 73 percent from the second. However, average sperm motility of the second sires was significantly higher (75.2% versus 55.1% in the first sires), so that may be a factor in that specific result.
There were some surprising results in factors that did NOT impact pregnancy or which sire’s semen prevailed.
Semen quality (progressive motility from 55-75%) did not seem to be a significant factor in the prevailing sire
Semen quality did not affect whelping outcome
Semen quality did not affect litter size
Semen quality did not affect parentage ratio
Age of the bitch or stud at mating was not a factor
Day of AI was not a factor
Number of inseminations was not a factor in parentage ratios
To sum things up, according to these studies, only about a third of dual sired litters have puppies from both sires. There's no good way to predict which sire will prevail, either.
Hopefully this will give you the information you need to perform informed dual-sired matings with confidence as well as with realistic expectations.
Lojkić, Martina, et al. "Dual sire insemination in dogs." Veterinarska stanica, vol. 54, no. 1, 2023, pp. 29-37. https://doi.org/10.46419/vs.54.1.9. Accessed 28 Jul. 2022. https://hrcak.srce.hr/274367
F.K. Hollinshead, M. Ontiveros, J.G. Burns, C. Magee, D.W. Hanlon, Factors influencing parentage ratio in canine dual-sired litters, Theriogenology, Volume 158, 2020, Pages 24-30, https://doi.org/10.1016/j.theriogenology.2020.08.030.