Multiparty dataset intersection count
This problem was studied under the name of private set-intersection cardinality (PSI-CA) by De Cristofaro et al. They give protocols for the two-party case both in the honest-but-curious and malicious setting, and the complexity grows only linearly in the size of the sets. A result for the multi-party case was given by Egert et al. using Bloom Filters.

In case you are interested in only testing whether two sets are disjoint without revealing anything else then the problem has been studied by Kiayias and Mitrofanova and under the name private intersection predicate evaluation.