Answer
Yes — a specific, known error can be caught and handled distinctly, rather than just via a generic WHEN OTHERS, provided that specific error is first associated with a declared exception name and its specific error number using PL/SQL's PRAGMA EXCEPTION_INIT mechanism. Declare a named exception, associate it with the specific Oracle error number the other event's error surfaces as (a numbered ORA-20xxx-style user-defined exception), and then catch that SPECIFIC named exception, rather than a blanket WHEN OTHERS, in your own event's exception-handling block — this lets you distinguish and specifically react to that one known error rather than blindly catching every possible exception the same way.