Group everything that beleongs to the text.
Open Window > Appearance
Click on the button "Apply new fill" in the bottom left of the panel
Drag the fill below the characters
While the fill is still select, apply Effect > Path > Offset path
Enter whatever you consider appropriate
In order to colose gaps inside the additional fill, add Effect > Pathfinder > Add
Then add Effect > Pathfinder > Divide
Double click that effect in the Appearance panel and uncheck the option "Divide and Outline will remove unpainted artwork"
Apply the effect > Pathfinder > Add
So you have 3 pathfinder effects there and two of them are the same.
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