Taken from the known issues list:
The proposed swap is interesting, but I don't think that turbine will provide extra hearts for the additional reincarnation.NEW: Hearts of Wood (including the +20 Heart of Wood that every character receives with the release of the Shadowfell Conspiracy) do not allow characters to have more than three classes during the reincarnation process, including "future" levels they haven't taken yet during the respec process, since DDO remembers what class levels you had prior to reincarnating even if the player intended to have only three classes by the end of the process. Swapping the class you don't want into one of your existing classes, and then performing another reincarnation to train into the desired 3rd class, can bypass this issue.
However, there's a possible workaround (which won't necessary work with all level splits):
Suppose you have a 11 Ranger/6 Monk/3 Artificer which you want to LR to, say, 11 Ranger/6 Monk/3 Druid.
As per above, it isn't possible to swap the 3 Arty levels for 3 Druid levels. But, you could take instead of the old arty levels Ranger and Monk levels until there are no Arty levels left. Then you are free to choose a third class again and fill up the remaining levels (former ranger and monk) with druid. This won't work if you back-loaded the Arty levels, and doesn't let you choose your class progression freely.