SQL> set serveroutput OFF
SQL>
SQL> begin
  2    dbms_output.enable();
  3    dbms_output.put_line('Hi');
  4  end;
  5  /

PL/SQL procedure successfully completed.

SQL>
SQL> set serveroutput on
SQL> exec null
Hi

PL/SQL procedure successfully completed.

SQL>

SQL> CREATE OR REPLACE FUNCTION DUMP_DBMS_OUTPUT
  2  RETURN sys.dbms_debug_vc2coll PIPELINED IS
  3          ln VARCHAR2(2000);
  4          sts NUMBER;
  5  BEGIN
  6          LOOP
  7                  dbms_output.get_line(ln, sts);
  8                  EXIT WHEN sts <> 0;
  9                  PIPE ROW (ln);
 10          END LOOP;
 11  END;
 12  /

Function created.

SQL>
SQL>
SQL> set serveroutput off
SQL> DECLARE
  2          i number;
  3  BEGIN
  4          dbms_output.enable();
  5          FOR i IN 1 .. 10 LOOP
  6                  dbms_output.put_line('Line ' || i);
  7          END LOOP;
  8  END;
  9  /

PL/SQL procedure successfully completed.

SQL>
SQL> SELECT *
  2  FROM   table(DUMP_DBMS_OUTPUT())
  3  /

COLUMN_VALUE
--------------------------------------------------------------------------------
Line 1
Line 2
Line 3
Line 4
Line 5
Line 6
Line 7
Line 8
Line 9
Line 10

10 rows selected.

SQL>