The sense inventory in DIMAP/NODE and ODE is identical and the most straightforward of any preposition to date. There are only core senses, no subsenses (although an arrangement in which some senses were subordinated to others would not be illogical; see the spreadsheet notes).
Notes from the spreadsheet:
New sense added: (Spreadsheet record 3) ODE makes no provision for a common use of into that is treated in other dictionaries. See, e.g., sense 3 in MW11 ("used as a function word to indicate a period of time or an extent of space part of which is passed or occupied *far into the night*") and sense 8 in Random House Unabridged " (used to indicate a continuing extent in time or space): lasted into the night." SRtype: PeriodEntered. Definition: used to indicate a period of time begun while some activity continues. I subsumed it here because the period of time in some sense "engulfs" the thing that appears in it. Even though there are very few FrameNet instances, those that exist cannot be classified elsewhere.
Other instances of into that may deserve idiomatic treatment
There are no phrases in ODE, and other dictionaries generally do not note phrases or idioms here. There is one slang sense, probably not likely to be encountered, nearly always followed by a for PP and indicating indebtedness: See, e.g., Random House sense 11: " in debt to: I'm into him for ten dollars."
I. ODE doesn't distinguish it but in many cases I think it would be useful to separate a sense for into that is currently subsumed under 7(7), ResultantState, "expressing the result of an action." From this you can easily break off all sentences where the action is of a dividing, separating, or classifying nature. The complement, in most cases, contains some number:
classify the asteroids into 16 groups
categorize your addresses into 5 sections
divide the students into two groups
Along similar lines, into often follows verbs of combination rather than separation:
combine the ingredients into a smooth batter
his ability to blend the parts into a decorative whole
merge two businesses into one
But these, to my mind, are more aligned with sense 6(6), "change of state." For our purposes, there's nothing to choose since these two share an SRType, but perhaps its worth noting that into often signifies the whole-to-parts and parts-to-whole transformation, and an ideal sense inventory might identify this as a single sense.
II. There is often little to choose among ODE senses 1 through 3, and sometimes even 4, with reference to particular FrameElements. I think this is largely because into really means about the same thing in all of these cases, and only the wording of the senses — and occasionally, nuances of the POA (usually a verb) — provides any basis for deciding which sense to slot it into. Element Goal is a good example of this phenomenon. The overarching idea conveyed by into is its indication of a process by which something formerly outside, not enclosed, independent, or unattached, becomes enclosed, bound, attached, or integrated: see the diagram at Quirk 9.15 for an illustration. Inevitably the assignments of into into various ODE senses require that the sense be a bit wider or more general than the current wording strictly permits — but this has been the case with many prepositions, and points up to the great usefulness of studying FrameNet sentences as a basis for making a prepositional sense inventory.