Just speaking literally, you go over a threshold. The only way you would go under a threshold would be in a game of extreme limbo.In English, at least. In Latin
limen,
liminis, means 'threshold, the head-piece or foot-piece of a door, the lintel or the sill'. (Our word
subliminal comes from it.) In Latin, it can also mean simply 'door' or 'house'. The post about Indian perceptions of threshold reminded me that in Latin a
fanum is 'an area dedicated to a deity', such as a sanctuary or temple.
Profanum means outside of this area. (Whence our
profane.)
Getting back to the topic, there is a word
supraliminal (
link) meaning 'above the threshold of consciousness or sensation)'. Maybe you could adapt that ...
[Edited: OK, I've fixed myself some coffee, and realized I'm just rambling here. Above the threshold is not what was asked for. Just move along, nothing to glean here.]