The most common and most likely answer to this crossword clue is the 11 letter word EXTREMITIES
I've seen this crossword clue in Financial Times
E
X
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More clues leading to the result EXTREMITIES
Buddy explains!

The straight part
We know that "what might be /di/gits" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what might be /di/gits = extremities.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EXTREMITIES mean?
EXTREMITIES noun- The most extreme or furthest point of something.
- An extreme measure.
- A hand or foot.
- A limb.