If the items to be dyed are 100% cotton and pale in color then, yes, one can overdye.
If the items are 100% cotton there are ways to discharge the colors from them.
One way is bleach, although bleach is detrimental to the fiber if left on too long. A cup of bleach to a gallon of water is a place to start, although I've used straight bleach on occasion (bleah).
Some colors don't discharge well either.
If you use bleach to discharge, you should use a product called "anti-clor" to neutralize bleach after discharging, obtained through ProChem or Dharma - also stores that sell aquarium supplies will have a product to neutralize bleach.
You should rinse the bleach off first before resting the items in the anti-clor water - then wash.
There is also a product called thiox:
http://www.prochemicalanddye.com/store/product.php?productid=16197&cat=249&page=2I've used this in the microwave and in a big pot, outdoors - it's smelly, but not like bleach.
You just rinse and wash after using this product.
k. taltre