We just stained our outdoor patio with Quikcrete Coffee Etching Stain. The coffee color turned out to be orange/rust color. Not what we intended at all. The question is... can we go over with another color of etching stain to get more of a brown tone? Or does anyone have any other suggestions?

Isn't the Quikrete a powdered version to added to the wet mix? Either way you can do as many colors as you want and I would advise doing at least two more dark brown or coffee colors. The beauty of acid etching the surface is that you can do multiple colors for a varied effect. Sherwin Williams has a decent brand with good color selections at my local store but Ive had mixed results with the sealers.
Here's our most recent floor with 3 colors; http://www.springtimehomes.com/files/img_2096w501014323.jpg

We did the same thing. Orange/Rust color. UGLY.

We did the tan color first and it was really orange, then we did the coffee color and it is a deeper darker color of orange/rust.

Unacceptable.

$150 worth of chemicals and thousands of dollars of damaged concrete.

I was going to answer but after reading Springtime I have nothing to say but great job.

Most brown acid stains will have an orange color after they have been applied. You don't really get to see the true color until you apply sealer. I cover this in my stained concrete guide. (https://voomly.com/decorativeconcrete) Here is a photo (http://decorativeconcretediy.com/wp-content/uploads/2013/03/sealacidstain.jpg) that shows a stained concrete patio while it is being sealed so you can see the drastic effect the sealer has on the final color.

Yes, I would also have to say what SpringtimeHomes just said. That would help in your situation and make your home beautiful.