In most cases, yes. However, some professional organizations which also have a social focus are single-membership (i.e. you can only join them, not also another "social" organization).
Also, just fyi, you can usually only join one within a specific field - for example only one music group.
There are also honorary Greek letter organizations. In some cases, you may be eligible for membership in several of these, even within the same career field.
Just to clarify - it is the Greek letters that make ALL of these "Greek." I am guessing you meant to say not social or general Greek.
For more information on many of the professional Greek organizations -
www.profraternity.org