Mia I hope I can make this clear enough for you to understand, I'm not good drawing little pictures to add to posts but here goes.

Instead of cutting 2.5" squares to sew across the corners of you strips that make the stars, cut 2.5 x 3" rectangles ( or longer if you want to 'float' your stars). Then sew them across the corner the same as normal but when you fold them over the extra length will give you more 'background'. This is like when you sew diagonal seams when joining binding strips, you need to sew carefully corner to corner so the strip opens out straight, and remember the extra length will need to be positioned in opposite directions on each 'leg' of the star. You will need to cut your corner of the block squares by the same extra amount so the block ends up square, so if these were 4.5" you will need to cut them 5", add on whatever the extra length was you added to the flip over squares.

I hope that makes sense, this can be done to many things and is good to do if you wish to 'float' your design so points don't come near the edge and get chopped off. It is used in many of the Mary Ellen Hopkins patterns/books. Mary Ellen pioneered the connector corner method and if you can get any of her books you will be simply amazed at what can be done.