Argument completions for string sequence

Question

I want to add completion for string sequence like

addCompletion[expr___] :=
    FE`Evaluate@FEPrivate`AddSpecialArgCompletion[expr];

list=Alphabet[];
f[x__String]:=(
    addCompletion["f"->{list}];
    {x}(*some codes here*)
);

Here addCompletion is from Argument completions for user-defined functions, and list stores some long strings that can be modified by some other functions.

But now only the first argument of f can be completed. I tried (and am not satisfied)

$fcompletion=4;

f[x__String]:=(
    addCompletion["f"->Table[list,$fcompletion]];
    {x}(*some codes here*)
);

Is there a method of completion adapted for __?