For m non-empty pairwise cross t-intersecting families of subsets of [n], the sum of their sizes is at most max{number of sets of size at least t plus m-1, m times Katona's bound}, with a complete extremal family description for t>1.
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Non-uniform pairwise cross $t$-intersecting families
For m non-empty pairwise cross t-intersecting families of subsets of [n], the sum of their sizes is at most max{number of sets of size at least t plus m-1, m times Katona's bound}, with a complete extremal family description for t>1.