I have dyed tone on tone fabrics many times. I have not however used Rit dye to do it, so have no idea how that will come out. I use fiber reactive dyes from Dharma Trading Company. Prewashed the fabric, with detergent - no fabric softener, then soaked in soda ash. I love the way tone on tones ( especially white on whites) come out. The nice thing about the fiber reactivate dyes is you can decide how long to keep it in the dye solution, control the extent of dyeing. I’ve used my own dyed fabrics for years they have been color fast with very little fading over the years.