In my humble opinion:
O has to give Room to M. But next M also has to give room to I. Hence, M has to address O for giving enough room to allow I the inside. Suppose M sussenly sinks and vanishes.... in that case I has no rights on O.  All is similar to luffin rights with more than two boats overlapped.. When the leeward starts to luff up, the next boat has to get the windward boat to luff as well - all within rule 15 allowing the other boat(s) enough to keep clear.

(Edit: I'm putting brackets around boat [I] to try to make it less confusing with the pronoun I.)

I don't think this scenario is particularly uncommon, and I have always understood it (and seen others apply it) as O gives mark room to M, M gives mark room to [I], and [I] rounds inside everyone. 

This is at least arguably consistent with [I]'s mark room obligations to O.  In a direct sense, it's not [I] that prevents  O from sailing O's proper course or sailing to the mark - it's the presence of M that prevents that.  I can see how if you squint a little at the rules, you could argue that I's rounding inside M causes O to deviate from proper course and course to the mark (and therefore [I] should slow down and round behind everyone), but I've never seen anyone argue that on the water or in a protest, and I don't think the language of the rules compels that interpretation.

Like Gijs said above, [I] would be in trouble if M was suddenly out of the picture, but it's usually safe to assume that M will remain in a position to insulate [I] from O.  

In a team race scenario, if O and M were on the same team and [I] was on the other team, a smart move by M might be to try to slow/stop their boat as soon as possible so that O can round ahead - M will still round behind [I], but that's better than both teammates losing [I], and O will be in a position to make a play on the next leg.  Alternatively, if M expects maintain overlap through the rounding, M could sail fast and plan to luff [I] immediately after the rounding.

I agree with Gijs as above, and that O has to give room for M to give room to I - but if it is not possible for M to give that room due to O,  then I suggest to read 18.2(f).

John

The definition of room requires the Outside boat to give the Middle boat enough space to comply with her obligations under the rules of Part 2, namely, to give the Inside boat mark room.

Definition Room

The definition of Room includes all obligations under Part 2.  Thus, a boat required to Keep Clear must "accommodate" all the obligations incurred by the boats she is required to give Room to.

I will assume that you are talking about a port rounding.

In general, the rules, including rule 18, apply to pairs of boats.  It is easiest to break situations up that way and consider each pair individually and then summarize the situation.

First let's review the definition of mark-room.  Mark-room incorporates the definition of room and, room is the space a boat needs, blah, blah, including the space needed to comply with her obligations under the rules of Part 2.

So we have three relevant pairs of boats, O & M, O & I, and M & I.

At the moment when O reaches the zone, M is overlapped inside of O.  As a result, O is obligated to give M mark-room..

At the moment when O reaches the zone, I is clear astern of O.  As a result, I is obligated to give O mark-room.  Also, we note that M is not a boat between and overlapped with both O and I at that moment.  If M & I were overlapped then O would be overlapped with I and obligated to give them mark-room.

At the moment when O reaches the zone, we don't know anything about M & I yet.  To apply rule 18, one of the boats of the pair has to be in the zone.
At the moment when M reaches the zone, I is overlapped inside of M.  As a result, M is obligated to give O mark-room.

As noted above, the mark-room that M is entitled to includes the mark-room that they are obligated to give I.  This means that O has to give M enough room for M to give I the room M is obligated to give I.  You can think of the obligations here as being additive.

Perhaps it is a rare scenario, not as Nicholas says because of the risky call of 18.2e, but because a tactical trailing boat (I) would hang back, sail wide, gybe, and cut in on a fast reach to round inside and higher than the dueling O and M.
How does Dave Perry say it "Free your bow"?

additional comment for those who are in to tactics (being a tactician myself) - O has not been playing its cards well winding up in this situation and loosing all. O should have taken the inside line way before when possible, otherwise O should have luffed up M still outside the zone and quicly bear away clearing the overlap on reaching the zone. Then O would have been fully clear of M and I, having a clean inside rounding based on Rule 18. It is quite ignorant as leeward boat in foul air to stay in this position that O has before Rule 18 comes into effect. Mark Roundings are Bermuda triangles where a lot can be lost, less gained. Wise tacticians would line up O-M-I and take the next battle in the upwind avoiding ambiguous protests and burdening umpires :-) 

Philip said: [Perhaps it is a rare scenario because a tactical trailing boat (I) would hang back, sail wide]
Sure that too, but it's certainly rare that boat I gets the overlap within the last 4/5 boat length to the zone and 18.2e isn't an issue.

Most responses so far ignore that I owes O room because she was clear astern when O reached the zone. That at minimum equals out that O owes M room to give [I] room. At that moment O is within two boat-lengths of the mark and is apparently suddenly receiving a new onus. That seems unfair and unsafe. How many boats can pile on in that way?

Gijs said: [Then O would have been fully clear of M and I]
You're not reading the scenario correctly. O is "fully clear" of [I]. [I] is clear astern and owes O room

@Nicholas

We aren't ignoring that fact that O is entitled to mark-room from I, it's just not relevant.  O's entitlement to mark-room from I does not change the room that O is obligated to give M.  By definition, the mark-room that O owes M includes any mark-room that M is obligated to give, in this case to I.  The entire fleet can pile in.

The obligations are additive, there is no canceling of obligations.  Think about it this way, if more than one boat was inside of O when they entered the zone, O is obligated to give mark-room to each one individually.  

Definition  " ... Overlap". They also overlap when a boat between them overlaps both. M has to give I mark-room as they are overlapped when M reaches the zone 18.2(b). Therefore O has to give M & I mark-room because she has to give M enough mark room to comply with M's obligations to give mark room, as M's proper course to the mark includes giving I mark-room (Def Mark-Room (a) & (b)). WS Case 114 Question 1 is exactly on point.

 Nicholas, maybe it would be illustrative to consider under what scenario would I’s MR obligation to O come into play. 

Let’s assume the following facts. 

In the scenario above… 

So .. you see .. I’s MR obligation to O doesn’t disappear … it’s just waiting to be operational and relevant.