Superadditivity conjecture for 2×4×4 experiments on Bell singlet pairs

A $2\times4\times4$ experiment is a Bell experiment with two settings for one party and four settings and four outcomes for each of the other parties. The experiment is performed on pairs of Bell singlets, with joint measurements allowed across the two copies. CHSH denotes the standard two-party Bell experiment used as the comparison.

Bell-pair superadditivity conjecture. There is an experiment on pairs of Bell singlets, of the $2\times4\times4$ type, more than twice as strong as CHSH, and involving joint measurements on the pairs.

This is a concrete version of the proposed superadditivity of statistical nonlocality under taking two copies. It is presented as a conjecture in the paper and is not established there, so it remains open.