I do this for tee shirts a lot. Especially the ones my friend machine embroiders a pretty design on them. I cut out the design, usually free form or a big rectangle and then raw edge sew it on another tee shirt. I starch and press both areas stiff and smooth and then sew. I usually match the color of the tee shirt. Machine embroidery takes a lot of thread and time to toss the design because of a stained or worn out tee shirt.