In 2003, Morales and coauthors published the broadcast/multicast-oriented Exclusion Basis System (EBS) that imposes low server and communication loads to securely broadcast new keys to the other participants after an individual participant leaves. This paper provides a method for dealing with multiple participants leaving simultaneously. In doing so it develops a general approach to encrypting messages to restrict them to a subset of participants defined by the keys they know as described by a logical expression. Difficulties presented by and countermeasures to collusion by EBS participants are discussed.