I would just put about an inch to cover the red mulch.

How deep is the mulch now? While I have put down 5 to 6 inches of mulch and have seen no problems doing so others have found that mulches too deep can restrict the amount of water reaching the soil.

kimmsr, they found that deep mulches restrict the amount of water reaching the soil? why, because the mulch holds a bunch of water and it was dry to begin with? I would think adding more water until it is soaked would solve the problem.

What kind of mulch are we talking about here? Bark? Wood chips? Whatever it is, you don't want it covering the crowns of perennials, so you'd do well to pull it off of them. You could cover it with another thin layer of something else if it really bothers you, but if the plants are going to grow in the next few weeks to conceal the soil anyhow, it probably isn't worth it. Or at least it wouldn't be to me, but maybe it is to you. I like to mulch with compost, which is dark brown to almost black and looks natural to me. It isn't the appearance that matters so much to me as how it improves the soil. I usually apply 4" or a bit more twice a year, but the amount that you may need depends on your climate, soil and drainage.

nil13, take a look at Natalies post about this issue.

Go ahead and add more mulch and let the perrenials have a little breathing room and don't cover them. I have found in my climate with high humidity, heat and rain, you can't have too much mulch. I like using leaf mould as my base mulch with hardwood mulch with a layer of pine straw on top of that.