Raising quotas forever is the trap, so the proper response splits into the immediate unblock, the sustainable arrangement and the systemic sizing, in that order:

The immediate unblock for the stuck user: quotas have three thresholds, warning, prohibit send, prohibit send and receive and a user fully blocked crossed the third. A temporary quota bump on that mailbox, Set-Mailbox user -ProhibitSendReceiveQuota, restores function while they clean up, the breathing room rather than the solution.

The sustainable arrangement, archiving: an Exchange archive mailbox, enabled per user, moves older mail out of the primary mailbox into archive storage automatically by a retention policy, keeping the primary under quota while the mail stays accessible in Outlook and OWA under an In-Place Archive node. This is the answer that scales, users stop hitting quotas because their old mail lives elsewhere by policy rather than by their discipline.

The user side cleanup that helps immediately: empty deleted items and the recoverable items dumpster, both counting against quota and clear the sent items attachments that quietly dominate most bloated mailboxes, the size sorted view finding them. Guidance to users beats surprise blocks, a warning threshold set low enough to prompt cleanup before the hard stop.

The systemic sizing decision: quotas set by role rather than uniformly, generous for genuine heavy correspondents, tighter for light users, with archiving underneath so the quota governs the working set rather than the lifetime accumulation. Storage planning follows from real usage data rather than the reactive bumps that got you here, the mailbox size report telling you where the mass actually lives.