Beretta 84 is blowback operated.
There are two classes of .380s. The classical blowback operated pistols and their modern offspring like the Walther PP/PPK, CZ83, Beretta 84, Sig P232, Bersa .380, and Colt 1908. Most of these pistols are single stack but some (Beretta, CZ) are double stack.
The other class is the locked breach MICRO .380s. These are usually considerably smaller than the "classical" .380s. These include the LCP, P3AT, Sig 238, Glock 42, and Kahr. To the best of my knowledge, there are no double stacks.
It seems like you want a gun more like the "classical" .380s but in double stack locked breach form.
To the best of my knowledge no such gun exists.
My suggestion would be a full size 9mm pistol.
Another option would be a classical .32 ACP pistol. They tend to shoot considerably softer in blowback form than their .380 cousins. The Savage 1907 is a double stacked .32 ACP that is svelte but allows a full hand grip and shoots very nicely.