What happens when two sperm fertilize an egg? This can be either naturally or by experiment.
This phenomenon is called polyspermy and results in an embryo which is not viable. This is because it has more than the usual two sets of chromosomes (one from each parent), but one from the mother and multiple (depending on how much spermcells enter the egg) from the father.
To avoid this, most species (including mammals) have protective mechanisms against it. The so called cortical reaction which starts upon fertilization (the first sperm penetrating the zona pellicula) and releases cortical granules to prevent further sperm cells from entering.
Although the results are fatal in animals, as Chris' answer explains, recent research has demonstrated that plants can produce viable offspring with three parents. E.g.:
- Triparental plants provide direct evidence for polyspermy induced polyploidy, Nakel et al., Nature Communications, 2017
We established a high-throughput polyspermy detection assay, which uncovered that supernumerary sperm fusion does occur in planta and can generate viable polyploid offspring. Moreover, polyspermy can give rise to seedlings with one mother and two fathers, challenging the bi-organismal concept of parentage.
This list of papers that cite the paper above includes more recent observations of triparental inheritance in plants.