DIMAP/NODE contain 11 senses for prepositional after; ODE contains 10. There is some rewording in some senses, but the only compelling difference is that DIMAP/NODE sense 1a has been absorbed into the core sense, which is logical. I have followed the numbering in ODE.
Notes from the spreadsheet:
New sense added: (Spreadsheet record 3, sense 1(1)-1) After very often means not only “following in time” (the core sense) but also “following in time and resulting from,” or in other words “after and because of,” which can serve as a definition. This is a serious omission in ODE. It corresponds neatly with many other prepositions introducing the reason for something and shares the SRType “Cause.”
Other instances of across that may deserve idiomatic treatment
All of the phrases in ODE are probably worth isolating because they don’t correspond to senses in the inventory except after hours, which is roughly 1(1). After all, meaning “in spite of indications to the contrary,” is a disjunct that does not correspond to any sense and should be flagged by the presence of a comma; but the complement is occasionally extended with not much shift in meaning: “After all I did for him, he still refuses to speak to me.” It might be sensible to treat “after all” as a standalone preposition, since whether or not a complement follows, it seems to nearly always carry the notion of “in spite of” – except in cases such as “after all the results were in, the winner was declared.”
There is considerable affinity between sense 5(2) Front, and sense 7(3) TargetOfPursuit; both normally entail one agent or object following another, and the only thing distinguishing 7(3) is that the reason for the following is pursuit; the POA is usually a verb that suggests this. Many verbs can be ambiguously used to suggest either pursuit, or mere following and only the wider context makes clear which it is. Logically then 7(3) would be a species of 5(2), which is quite general (basically, =behind), but this is not how ODE has organized the senses, and I’ve kept their shema intact.
Only half of the ODE senses (plus the sense I added) are exemplified in FrameNet. Senses 2, 3, 4, 8, and 10 in ODE, all reasonably common, have not been picked up by the FrameNet parsers, despite their all being fairly common.