"Successful" triads from our experience most often just fall together almost accidentally. Trying to create one by design seems to have poor results.
So by the same note, "unsuccessful" triads - or any relationship - often are the result of design & specifications.
It seems the best concept is just to be open and aware as people come in and out of our lives. Things can spark and grow totally unexpectedly. But first you have to notice them, then nurture them.