For m non-empty pairwise cross t-intersecting families, the sum of their sizes is at most max{sum_{k=t to n} binom(n,k) + m-1, m M(n,t)}, with a complete characterization of the extremal families.
Frankl, On the maximum of the sum of the sizes of non-trivial cross-intersecting families, Combinatorica 44 (1) (2024) 15–35
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Non-uniform pairwise cross $t$-intersecting families
For m non-empty pairwise cross t-intersecting families, the sum of their sizes is at most max{sum_{k=t to n} binom(n,k) + m-1, m M(n,t)}, with a complete characterization of the extremal families.