The sense inventory in ODE and NODE/DIMAP is identical.
Notes from the spreadsheet:
No senses were added. There is little distinguishing the senses that are present, and three share the same SRType.
Other instances of above that may deserve idiomatic treatment
All of the phrases in ODE in fact fit into senses in the inventory: above all (else) is sense 7(2c) ThingNotPreferred; from above, as figuratively defined here, is 5(2a) ThingOutranked, though it could and is often used literally (“from above the rooftop we could see . . .”), in which case it fits one of the ThingSurmounted senses. Finally, above oneself and not be above (sth) are both 6(2b) InferiorObject. It is probably worth isolating the construction not + ppabove as this is probably most of the time this idiom: “He’s not above lying to get his way.”
Except for one sense, 6(2b), all senses of “above” can be seen as species of “over” and are often used interchangeably with them. Sense 9(3) Norm of above is for some reason defined more specifically than over sense 10(3), but in fact they can also be used interchangeably. I have, however, for now given this above sense a different SRType because of the wording of the def.