I consulted the BEAST authors, who kindly gave me the official solutions. Here are how it should be done:

Edit the xml file. In state code section, create ambiguity definitions like:

<generalDataType id="fruit.dataType">
        <state code="Asia"/>
        <state code="Europe"/>
            ...
        <state code="Antarctica"/>
        <ambiguity code="Eurasia" states="Asia Europe"/>
</generalDataType>

Then go back to taxa section, set the code of desired taxa as "Eurasia".

Then go to treeLikelihood section, set useAmbiguities="true".

Hope this is helpful to people who read this post.

I haven't tried this in BEAST yet, but my analysis works fine in PAUP and MrBayes for multiple character states with parentheses: in your data matrix, for example, you will have (Asia,Europe) for character uncertainty or {Asia,Europe} for both character states. Give this a try.

I do know this designation will not work using the read.nexus.data script used by ape in R. In that case, I've either added a separate character to my data matrix or coded my data as continuous, which both have data analysis disadvantages downstream.

I don't know of any software that deals with a taxon taking multiple states for the same character, but do you really need to code it this way? Why not make "geography" a presence-absence character:

       Asia    Africa     Europe
sp1      1        0         0
sp2      1        1         0
sp3      0        0         0

edit the other option to consider is dreaming up some discrete-character model (eg rev) in which each possible geographic combination is represented by some rate of change that reflects the fact that changing from, say, Asia-Africa -> Europe-Africa-Asia is much more likely than going Europe -> Europe-Africa-Asia... though this seems like a lot of work.