Yes you can.

But sorry for asking, is it gonna be a big bag and if so, are you planning to use it in transit?

If you are not and you are planning to stay outside of the airport, then you can check that extra piece later.

(But do take note if that extra piece might turn out to be excess luggage for you if you are travelling within Asia where they go by piece and weight, some airlines and extra-alert check in staff might take note and decide to charge you for excess luggage)

Years ago, while flying on United out of Terminal 1, I was able to get make an arrangement with SIN Immigration for me to get my luggage from the carousel,(just one piece tho) bring it back inside to the Transit hotel, and check it again at the gate. Tho cumbersome, it did work.
I am not too sure under current climate you can bring it with you into the transit are if that is what you plan to do.

Otherwise bring along a reasonable sized handcarry with things you need for a short layover and you will be fine.

Cheers!