Based on the current (rather expensive) I class fares - it would appear so with a $100 surcharge for the 2nd 'stopover'.
Fare basis IRCG ex CNS/OOL/MEL
[CODE]3 STOPOVERS PERMITTED IN EACH DIRECTION
LIMITED TO 1 FREE AND 2 AT AUD 100.00 EACH.[/CODE]
and
[CODE]001 CNSJKT 16JUL24 QF AUD 4910.00 IRCG STAY---/12MBK-I
FARE CLS EXPLANATION BOOK CODES
-------- ---------------------- ----------
IRCG BUSINESS CLASS ADVANCE PURCHASE FARES I
IRCG BETWEEN S.W. PACIFIC AND SOUTHEAST ASIA FOR ROUND
TRIP FARES
BOOKING CODE EXCEPTIONS
VIA QF I REQUIRED WHEN AVAILABLE WITHIN AUSTRALIA
VIA QF J/B PERMITTED WITHIN AUSTRALIA[/CODE]
Just to clarify - I believe you need to find dom legs with no I class for it to bump up to J.
This can be easy on routes like SYD-MEL - last week I booked a DPS fare and was able to find an I0 MEL-SYD departure on the date I wanted to travel in Feb 2025. But this might be more difficult on typical leisure routes, especially more than 6 months out.