  We initiate the study of simultaneous core multipartitions, generalising
simultaneous core partitions, which have been studied extensively in the recent
literature. Given a multipartition datum (s|c), which consists of a
non-negative integer s and an l-tuple c of integers, we introduce the notion of
an (s|c)-core multipartition. Given an arbitrary set of multicore data, we give
necessary and sufficient conditions for the corresponding set of simultaneous
core multipartitions to be finite. We then study the special case of
simultaneous core bipartitions, giving exact enumerative results in some
special subcases.
