The idea of stressing down species barriers is to use environmental stress to break down any barriers that prevents hybridization between different organisms (maybe even as far apart as a human and a plant) by environmentally stressing the cells so that they lose their cellular xenophobia.
Why this may workEdit
There is evidence that yeast cells spontaneously start living collectively when centrifuged for 60 days or so, as shown in "Key step in evolution replicated by scientists". I could not afford such an expensive centrifuge, but when I heated and cooled the yeast it became multicellular in about a day. I checked the transitional stages under a microscope and saw that multicellularity formed by making the cells too weak to fight each other.
Connecting to the experimentEdit
Given that environmental stress breaks down cellular xenophobia, this may well apply to hybridization barriers as well. There is genetic evidence for mosaic character of some organisms, especially among marine animals. The trick is to environmentally stress oozytes until they let in sperm (or pollen) from completely different organisms. Environmental stress can be provided by centrifuging, temperature fluctuations, or maybe by suitable chemicals. This may produce some really weird new forms of life!