The baggage can be checked through, but will likely require a manual baggage tag (and an Agent who knows how to generate one), due to a triple connection.
I would absolutely not recommend this...
Earlier this year, UL in SIN had difficulty issuing (but eventually they found out how to do it) SIN-CMB-FRA-CPH-BGO and they said there will be 2 baggage tags.. I thought, er, no, more margin for errors and misconnection.
So I checked it SIN-CMB-FRA and then rechecked it from FRA-CPH-BGO.
These were on separate tickets.