A hinged day bed would be easy in a TD.
Wish I was more computer literate and could use auto cad or even add a drawing.

Remember keep it "Simple"

I would build a second floor layer (1/2" plywood) as my day bed. Cut into 3 pieces ( 24" , 24" , 28" for TD with an 80" long floor inside)secured together by 2 piano hinges. At he head end I would have a cross shaft or two deadbolts (1/2" diameter) that locked into the inside walls on either side 4" forward of the headboard (to accommodate a 4" mattress).
At the foot end I would install three 3/4" wheels (one on each side and one in the middle) to allow the bed bottom to move smoothly when reconfiguring to the "day bed" position. A handle on each side would be helpful too. Two more dead bolts or locking pins (as stops) will be required at the foot end to secure the hinged floor in the desired up position (depending on the angle you like your back rest).
The Mattress will be cut into tree pieces accordingly, and can be left as separate pieces or hinged together by a sewn mattress cover, allowing it to follow the floor up and over the back rest.
There! Is that as clear as mud?

Hope this was of some help.
Maybe someone with drafting skills could draw this up for us?
Good Roads
Brian & Sandi