Are the gutters and downspout clear? Is the water puddling on the stoop and backing up over the threshold and under the doors?

Get rid of the double doors and replace it with a single door with sidelites. Double Doors with no overhand equals a leaker every single time.

Gutters are clear. And yes we are considering adding an awning. Don’t love the idea but I can’t think of a better solution. Would probably prefer a period overhang but can’t find good ideas..

Ask an architect. They have access to all kinds of great ideas.

You might benefit from replacing the existing gutter with a larger size which can handle a greater flowrate. That might require an additional downspout as well.

I'm sure you've explored everything for ideas already, but posting these just in case. I think they are all nice looking and pretty unobtrusive. Your home is fabulous!!

Copper Mediterranean Door Awning

I'd even skip the stripes and bold color in pic below and just have the fabric the color of the stucco.

Cut a riglet into the stucco and have the flashing cover the door casing with a rain kick-out. It will be inconspicuous after painting to match. Something like this:

My door shop once told me doors need overhangs. That solved many problems.

Some hinged doors survive OK without if they have a robust door sealing system. The Anderson's I've installed have always been great.

Your doors open out so the water may be going in directly on the top of the door and the seal isn't holding. The center seals are also issues if the doors have any warp. Check the bottom seals.

How old are the doors? Please take photos of the door 4 edges and jambs.

Likely the solution involves more cover and/or new door systems, likely higher end.

Thanks. We have decided to add awnings to the doors. Not my favorite but we have too. The doors are only 4 years old. But yes the water comes directly on the top and also bottom. We have changed the seals and it hasn't helped. And i want to be prepared for this winter... Thanks

Post us a pic when you have them up.