For a routine ask of a colleague, yes — it over-softens. "Could you" is already polite in native US, UK, and Canadian English, so adding "possibly" doesn't add warmth, it adds doubt. "Could you possibly send me the file" reads as if you expect a no, which can make a fluent speaker sound unsure or junior. Just say "Could you send me the file."
Many capable non-native speakers learned that more softeners mean more politeness, so they stack them. But "could you" already carries the courtesy for a reasonable request between peers. "Possibly" then questions whether the favor is even fair to ask, so the request lands as tentative rather than considerate. The issue isn't that it's rude — it's that you sound like you're bracing to be turned down.
This is a register problem, not a grammar one. "Could you possibly" is perfectly correct, and it has a real use: genuinely big or awkward favors. The mismatch is using that heavy hedge for a normal, reasonable ask, where it reads as over-soft.
Drop "possibly" when the request is routine and reasonable:
Instead of
"Could you possibly send me the deck before the call?"
Write
"Could you send me the deck before the call?"
"Could you" is already polite for a peer; dropping "possibly" makes a routine ask sound confident, not cold.
Instead of
"Could you possibly take a look at this when you get a chance?"
Write
"When you get a chance, could you take a look at this?"
The "when you get a chance" already softens the timing, so "possibly" just stacks doubt on top.
Instead of
"Would it be at all possible for you to review the doc today?"
Write
"Could you review the doc today?"
A direct ask with a clear deadline reads as organized; the heavy hedge reads as unsure the request is fair.
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