I believe Jim is right, but it took a little cogitation and a diagram or two for me to work out why he's right. Far longer, in fact, than I would've had in the real world, which is half the point. An interesting situation, and the Case book doesn't quite cover it. Perhaps Case 124 is the closest, but Case 11 is also relevant.
In this case all boats are on Port, so Rule 10 does not apply. The beating boat (B) will be to leeward of both the others (W and L), and therefore has right of way over both W & L. B is an obstruction to both W & L - 'A boat racing is not an obstruction to other boats unless they are required to keep clear of her' - but it is an obstruction if they are.
19.2(a) allows a right-of-way boat to pass an obstruction on either side. L can choose to avoid the obstruction by sailing either in front of B or by ducking its stern. As leeward boat L has right of way over W, but because L gained its leeward overlap from behind it is restricted from sailing above its proper course (Rule 17).
If L chooses to duck B's stern, and W follows, L becomes the outside boat and does (if hailed) have to allow W to duck B's stern. But as right-of-way boat over W, L can also choose to pass in front of B. (The definition of 'Proper course' does not imply the absence of all other boats, only 'the absence of the other boats referred to in the rule using the term'. In other words, if W were not present, B would still have been beating to windward, and L would still have had to make the same choice about B; L's proper course might have involved luffing in order to pass safely in front of B.) In this case L would be the inside boat, and W has to give room as both outside boat and as windward boat. If L needs to change course by luffing in order to pass in front of B, it is still sailing its proper course, albeit one changed by the imminent arrival of B, and W has to avoid L. W cannot assume that L is going to duck B's stern; L has to wait until it sees L heading to duck B's stern before calling for room.
Over to Brass to put us all correct.
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