Is DNA from more parents (than two) better for the fitness of the offspring?
There are very many details to address in this question. I will try to keep it brief and keep the scope of your question in mind, which is rather narrow. I also think your friend is over-simplifying and misleading you, assuming he is honest about the explanation he gave you.

We are talking about sexual reproduction, correct? Firstly, with 3+ parents:


it's not obvious that you will have "more diversity" in the DNA, nor that
"more diverse" DNA will be a cause for increased fitness.
Additionally, it would take a whole lot of machinery and evolutionary happenstance at the cellular and molecular levels to recombine DNA from 3 or more parents to make a stable, recombined genome, and this itself may introduce more problems than solutions.
More so, you're implying that a sexual organism that requires mating between 3 or more individuals will be fitter than an organism born of fewer parents. This is subject to whether the gain in fitness of having more genetic parents will outweight the cost of maintaining such a system. This would certainly be dependent on the environment, the population, and all the nasty little details of life, such as how mate choice would work, whether a backup for 2-individual mating would exist, etc.


Remember that fitness is a probability of obtaining a number of offspring rather than the number of offspring. I think it is self-evident that the requirement for more parents, rather than less, lowers the probability (i.e. fitness).

This is quite a hypothetical discussion. In nature, for all its ever-experimenting and ever-diverging forms of life in the last 4 billion years, we find no organisms with more than 2 sexual parents. Take this as a sign that the natural occurrence of this kind of system is probably not favorable to survival and reproduction.

And I realize we could discuss this topic on many fronts (I have a few more ideas that I omit here), it's a rich question to digest.