Some shows specify in the cast breakdown "with doubling" or "flexible casting".... language to that effect.

The example of "The Dining Room" was brought up as one such show.  It is traditionally performed with several actors taking on multiple roles.  So is "The Laramie Project".... and "How I Learned to Drive". 

From Dramatists website, here is the link to "The Laramie Project": http://dramatists.com/cgi-bin/db/single.asp?key=2955

And, "How I Learned to Drive": http://dramatists.com/cgi-bin/db/single.asp?key=2683

And "The Dining Room": http://dramatists.com/cgi-bin/db/single.asp?key=1279

It's pretty clear for these shows that flexible casting/doubling is okay (in fact, encouraged).

Obviously, plays that are in the public domain (such as Shakespeare and Wilde) can be cast any which way, as no copywrights are in effect.

With regard to shows which don't necessarily specify if doubling can be used, if you're not sure, then perhaps your question can best be answered by inquiring at the publishing house.