I think they do that Ann, I've seen one which looked like it was collecting it's web. I don't know how they would rearrange the strands if they do that though, they are very sticky.
I have watched a spider making a web, they can move very quickly and make a good web in a very short time. I had an Araneus diadematus female inside my kitchen window, she had been living there since she was a tiny spiderling and had made some threads to catch her prey on the wall/ceiling. When she got big I thought it was time to put her outside, but we had some mild weather and I left the window open a tiny bit and she made her way back in! Late at night there she was, zooming from the corner of the window (she had lived in the middle at the top) down to the window ledge to peg her web. It was made in a jiffy and I didn't have the heart to move her again. Towards autumn there was barely an insect coming inside so I worried she wouldn't get enough food so I had to put her outside, there was another spider outside on the window top getting more than it's fair share.
