We consider secret sharing schemes which, through an initial issuing o
f shares to a group of participants, permit a number of different secr
ets to be protected. Each secret is associated with a (potentially dif
ferent) access structure and a particular secret can be reconstructed
by any group of participants from its associated access structure with
out the need for further broadcast information. We consider ideal secr
et sharing schemes in this more general environment. In particular, we
classify the collections of access structures that can be combined in
such an ideal secret sharing scheme and we provide a general method o
f construction for such schemes. We also explore the extent to which t
he results that connect ideal secret sharing schemes to matroids can b
e appropriately generalized.