Two-parent sexual reproduction gives a maximum of a roughly 50% increase in the progeny's genetic variability over binary fission. To add a parent and have three parents, you get at most a 66.6% increase in variability, with four parents, you get a 75% increase in variability, with five you get an 80% increase in variability, and so on. This approaches a limit of 100%, but never gets there.
The actual increase in variability depends on the differences between the parents.
However, having all these additional parents has a cost in that they must be mustered to provide their genetic material at the appropriate time, and the more parents, the harder to arrange.
So, from an evolutionary point of view, the greatest advantage comes from 2-parent reproduction, and with the diminishing returns and additional complexity of higher numbers of parents, having higher numbers of parents is of a lower degree of fitness than just two.
However, evolution is 'survival of the adequate', so if a three-sexed reproductive system occurred in the absence of a two-sexed system, it would likely provide sufficient advantage to be retained in future generations. However the likelihood of this is quite low, but not beyond the bounds of all probability.
In addition, such a three-sexed reproductive system would be vulnerable to competition by newly occurring two-sexed species which can reproduce faster and more easily.
It is generally not possible for a female to provide 50% of DNA and for an arbitrary number of males to provide parts of the other 50%.
You may have a situation with a genome having a ploidy of 2N, where male and female contribute equal amounts of DNA (N each).
With a ploidy of 3N, the female may contribute 2N and one male contributes N, or the female and each of two males contributes N, or the male 2N and the female N.
With a ploidy of xN, (where x > 3), there are many combinations of what multiple (m where sum(all m) = x) of N the female and each male involved (up to x-1 males) contributes. You cannot have an arbitrary number of parents; the system will dictate that there are specific numbers of each sex involved.
To violate ploidy typically results in either death of the offspring or a greatly reduced fitness.
Consider bananas: the ones we eat have a ploidy of 3N, resulting in the seeds being very small and infertile. Otherwise, if we were eating 2N ploidy bananas, we'd be spitting out the pips. This means that cultivated bananas cannot generally reproduce without human assistance. This is a typical minimal consequence of violated ploidy.
Another example is chickens: They are typically 2N, but they can reproduce parthenogenetically, resulting in N offspring, which are - on the rare occasion when they hatch at all - considerably less healthy than their parent.
Since evolution will typically configure an organism to have a certain amount of genetic material, having 50% from a female and 50% from an arbitrary number of males would require some sort of mechanism to select which parts of the male 50% to take from each of the arbitrary number of males. This is highly unlikely to evolve naturally.
If such a reproductive system was to evolve, having 2 parents would provide a 50% advantage in variability as normal, 3 would provide at most 62.5% advantage, 4 would provide a 61.11% advantage, 5 would provide a 51.56% advantage, 6 would provide a 50.16% advantage, and so on, approaching 50%.
I had to run these numbers several times to verify that they were correct; it seems that the advantage is greatest with two fathers, and actually decreases thereafter. It seems counter-intuitive, but that's how the math works out.
It is more likely that if an arbitrary number of males contribute to the genetic makeup of a female's offspring, having 1 male parent would result in 50% of the offspring genome originating with the female, but having 2 males would mean that the female and each of the males contributes 33.3%, or 3 males means that each parent contributes 25%, and so on.
In the latter situation, the more males fertilise the female, the less the offspring would be related to the female, and hence it would not make evolutionary sense for the female to allow more than one male to mate with her.