I almost pasted in your photo so everyone didn't have to go the link route, but I noticed all your photos are © all rights reserved. So I didn't. That's a smart thing to do by the way, ©.

Your screen door is very smart looking. There are a lot of doodads out front: the flower on the door, the big pot of plants, the flag. If you get a new color on the door that you love, I wonder if there will be less doodads and decoration. :~D

I can think of one color for the door. It's a red, but it is a very warm red. "Warm" red is a big clue that it is an orange-y-er red. I know you don't want "orange" but the bricks are going to dictate to a great extent the color choices. Also, you don't want the door color to blend any more, like the current color. So, to get that punch you're likely lookin' at some flavor of red.

Ben Moore's Caliente would be the first chip/sample I'd check out.

Another idea to play with is something like a mid-value golden yellow. Again, due to the brick you'll have to get the *right* golden yellow, but it is another color option that will pop and not blend.

The color that comes to my mind is a teal blue/green. I don't have a specific brand/name in mind. In general, if you want something to pop then you would think of using complementary colors. Since you're in the red/brown category with the brick, the teal would pop but still not look crazy.