DIMAP/NODE have six senses for this preposition; ODE has five. The fourth ordered sense in NODE (numbered 32 in DIMAP) is eliminated, and presumably subsumed under the previous subsense in ODE . There is in fact minor rewording in all of the senses. As usual I have followed ODE’s numbering.
Notes from the Sense Analysis Summary:
There is no separate spreadsheet; all senses are added to the SAS, as they have no particular anomalies.
Other instances of down that may deserve idiomatic treatment
Most of the phrases in ODE would not be parsed as PPs because of other syntactic considerations. Numerous phrasal verbs have “down” as a particle; in many of these, down has no literal meaning. The transitive phrasal verbs among these (e.g., live down, put down, shake down, and many others) could be falsely parsed as down PPs that would not make much sense according to the ODE inventory.
There are also numerous idiomatic phrases that begin with down (“down memory lane”; “down the drain”; “down your/etc. way; “go down that road with sb,” etc. These are in fact PPs but do not reveal there meaning if parsed without reference to the governing idiom. Most of them have a limited range of POAs, which may help to disambiguate them.
Other notes:
As a spatial preposition, down seems to always mean the same thing: movement or placement further along something that can be conceived linearly. ODE divides the senses according to whether the complement is essentially vertical or sloping and/or the POA verb conveys the idea of descent (sense 1); a water course (sense 2); or anything else (sense 3). The only other senses defined in ODE are a dialectal British one equivalent to at or to (sense 4), and a temporal sense (sense 5). FrameNet has no instances of senses 4 and 5.
Many instances of down in FrameNet are adverbs, and in this capacity, down does about the same job as it does prepositionally, that is, indicating movement or placement as noted in senses 1, 2, and 3. Some of the many instances of down adv. are followed by a PP: down to the river, down into the mine, down onto the animal’s back, down across a steep slope, down from the seat. These are marked (adverb) in the instances file; most of them are related to sense 1(1), with a few related to sense 3(1b).