While watching TGS Outdoors Inside a Hunting Fair-Cacccia Village 2023 at about 22:28, a Beretta host demonstrates a trigger group that can be installed in 680-690 series O/Us, that features a double trigger but with the added feature that either of the triggers can fire both barrels without moving to the second trigger. You pick the trigger corresponding to the barrel one wants to shoot first and then pull it again to discharge the second barrel. This is similar to what Browning once had on the Superposed. Here's a link to the Beretta site:
https://estore.beretta.com/en-gb/pr...er-for-serie-680-ga-20---28---410-E02485