Hello! I'm traveling JFK-FRA-SIN in business class in June, and since I am relocating back to Singapore, I have a lot of baggage with me.

From what I understand, my check-in baggage allowance is 23kg x 2 pieces. But I have a 3rd piece of luggage that I would like to carry with me, and I was wondering if I could do that through SQ's unaccompanied baggage service, and for how much? Would you guys also have other alternatives to suggest, other than mailing it through USPS/Fedex/UPS/DHL?