Transenlightenment is a term I originally coined (in 2006) to refer to states of Realisation and Divinisation that are even beyond conventional Realisation ( formerly "Enlightenment"). It corresponds to what Sri Aurobindo calls Intuition, Overmind, and Supermind (and maybe also levels below that but still above conventional liberation such as Higher Mind and Illumined Mind).
In Letters on Yoga (page cit. to be added) Sri Aurobindo refers in passing to Ramakrishna as pertaining to his "Intuitive" level, which (if true) would make Ramakrishna a Transenlightened Guru by this definition.
He also mentions (ref to be added) that some inspirations in the Intermediate Zone are from the "Higher Mind" level. This may explain a strange mix of wisdom and delusion in Intermediate Zone gurus, and also their tendency to see themselves as avataric figures beyond even liberated and Realised beings. Of course, in their case these insights are mixed with false light, narcissicism, and delusionism, and hence the authentic element is so distorted as to be actively misleading. This also shows the ways that all these realities interact and overlap. It is very misleading to put things in specific boxes or yes/no categoriues.
Since contacting Ramana Maharshi's Light I also came to an alternative definition, which is that Transenlightenment could correspond to the avataric state. A Transenlightened guru therefore does not necessarily have to be tapping into the planes above mind that confer integral realisations. He or she could be also or alternatively embodying the Supreme from behind creation.
I no longer use the term "Transenlightened", preferring just Realised or Awakened. For regardless of whether one Ascends or abides in a Nondual state these are just different aspects or facets of the same Supreme, just as two such very different teachers as Ramana Maharshi and Sri Aurobindo embody the same Transcendent Supreme.
Update: (26 Nov 09) well, I have changed my views again, and come full circle (although hopefully on a higher turn of the spiral! I now describe various stages of Transformation, including Realisation, Higher Realisation, Divinisation, and Higher Divinisation, which are equivalent to various hypostases, which in turn are inspired by Sri Aurobindo's Spiritual Mind, Overmind, and Supermind
Nevertheless, I haven't resurrected the term "Transenlightenment", the reason being that "Enlightenment" itself is now a meaningless term, and most people who call themselves "enlighetned" are either self-deluded (on the basis of some inner experiences), "translucents", or both. While such people may indeed be sincere, teh temptation is too great to become an abusive guru. And if there is fake Enlightenment, why not fake Transenlightenment? Therefore, I developed a new hjargonb, using less familar terms like Realisation with a capital "R") and "Divinisation" , and emphasising individual, collective, and cosmic transformation over setting oneself up as a spiritual teacher. Again, I do not wish to any way question or dispute the sincerity of and good work done by many sincere spiritual teachers, but only to adopt a new terminology which should be rogorously used. Even though, no doubt, this will end up being abused like the old New Age terminology! In which case, either the word has to be rescued from its misinterpreters and reinterpreters (as i have tried to do re "integral", in an evolutionary manner) or a new jargon formulated.