Enable/Disable Trigger per single transaction

Assuming we have well over 1000 users accessing the database through a web
application.
We have a row-level trigger set up on table "alpha" that gets executed after
updates.

I was wondering if there is a way to temporarily disable a trigger on table
"alpha" for a single user, even though there may be 999 other users sending
transactions to the database that need the trigger to remain in place?  For
example, I only want the trigger disabled for one single transaction (using
commands inside that transaction) while the trigger still gets fired
properly for the other 999 transactions that hit the database
simultaneously.

Is this possible at present?

Thank you for your insights,
Derrick