I've looked through your archives, and can't find this question answered, so thought I'd write you. Is there anything wrong with putting on one LONG warp, and using it to weave many different things? For instance, I currently have on a 15-yard, 22-inch wide, warp using 8/2 variegated blue/green/brown cotton, relatively closely sett at 24 epi to make plush kitchen towels. ( I like to use variegated yarns as they allow me to vary the colors in the weft.) I've looked at quite a few shawls and they are just about the same width – so couldn't I pull out my stash of blue and green cotton chenille (which isn't strong enough to use for warp threads) and weave a shawl on the same warp? Do you think the drape would be soft enough?
There is absolutely NOTHING wrong with weaving more than one item on the same warp. You can, of course, weave many towels on your warp (as you are doing), leaving the sett exactly as it is and using the same weft yarn you are currently using. But what you are probably asking is: Can you weave a fabric with an entirely different intended use/fabric hand on the same warp?
In this case, you have to think about how to get the fabric hand that is required by the item you want to weave. You wouldn't want to weave a shawl that felt like a towel. A chenille weft will help change the fabric's hand to become more shawl-like, but your warp sett is too close. The chenille won't show or really be felt very much. So, after you cut off the towels, I'd resley the the warp to 15 epi as a first try (the shawl will be wider, but that is fine for a shawl), and then weave at about 15 ppi with the chenille. I'd start with about a 6" sample, cut it off, and wash it to check the effectiveness of the setts and yarns and make any changes necessary. 8/2 cotton is not a yarn you'd usually choose for a shawl, so you'd have to see if you can get a hand that will work. If it doesn't, you'll probably think of something else to try.
I always recommend putting on long warps, much longer than your planned project. As you are weaving what you planned, other ideas will occur to you, sometimes for different weft colors, sometimes for different types of fabrics, sometimes for different treadling orders, sometimes even for entirely different threadings/weave structures. As you use the yarns, your observations about how they look and feel will give you new ideas that would not occur to you just by seeing a yarn on a cone.