I've done this flight on Qantas (BNE-SYD-BOM) and the Royal Jordanian (BOM-Amman-CAI). However there is an about a 7 hour stopover in BOM which is never nice.
As you are including a DXB sector, this will mean you will probably have to purchase the CAI (or AMM)-DXB sector as a separate ticket and backtrack thru CAI (or AMM) to catch your flight back to BOM.
Alternatively MAS (using an Egypt air codeshare) and SIN both fly to CAI. Unfortunately neither fly via DXB (MAS did fly via DXB when it was on MAS metal - too bad)
Anyhooooo, if it was me, I would fly Emirates (or
Etihad) all the way.
If you want to keep it *Alliance then I'd fly:
SQ to DXB and then Egyptair to CAI.
OR
TG to DXB (or BKK) and the Egypt Air to connect from DXB, You can also fly TG all the way to CAI from BKK on a Egyptair Codeshare.
OR
SA PER/SYD-JNB-CAI (surprisingly good connection) and then Egyptair-DXB. Has a long backtrack home though.
If you want to fly One World then CX (or JAL) to DXB and then RJ to CAI.
RJ also fly brom HKG and BKK too AnM amd CAI.
KISS: Emirates.