Thailand to Singapore - separate tickets?

I'm booking a trip to Thailand and Singapore from NYC. The one-way tickets add up to around $1.4K total.

HOWEVER, there is a tempting premium economy option that flies from JFK to Changi round trip for $1300, plus $200 for a one-way flight to Bangkok via the same airline (Singapore Airways). Thailand is the first leg of the trip and the extra flight is booked separately from the round-trip itinerary.

Would this be risky since these flights are booked separately? Or would the fact that it's the same airline not make a difference?