http://www.scientifi...asexual-lizards Here's a real world analogy for the Asari and how they reproduce.As far as I can tell Interspecies reproduction would work one of two ways with Asari.
1.Linking Nervous Systems randomises the chromosome pairs the Asari uses to reproduce,and which is already present in her body.
2.They take DNA from their partner and use it to randomise the chromosome pairs or generate new pairings thus strengthening their genetic diversity.
Personally I think it's 2,since DNA is obtainable from a myriad of sources,even saliva,so they could then breed with anyone.Also the Ardat-Yakshi is a genetic disorder present only in Pureblood pairings so again the Asari cultural edict of interspecies pairing would make sense.By mating with non-Asari they broaden their genetic database and equip the species to better survive.