Can you put non permanent hair color over permanent hair color with out any weird effects?

My natural hair color is a light mousy brown. For the past year my sister has been dyeing it Light Auburn (Revlon- ColorSilk- #53) and Black (Revlon- ColorSilk- #20). I really like the Red and Black, but I’d like a temporary change. I bought some non-permanent brown color (Clairol- Natural Instincts- Loving Care- #765) that says that it lasts for 6–12 shampoos. I was wondering if I use the non-permanent, when it washes out, will it effect how the red in my hair looks? And on that note, will the permanent hair color effect how long the non permanent color takes to wash out? Like I said before, I really like the red and black and I want to keep it, but I’d like to see what I’d look like with brown hair.