Are you talking about a covered porch? A screened porch? It looks like you already have an “outdoor living space” in your patio.

Could you post a plan for the size of the patio . It needs to be a lot bigger than it is, And is this going to just have a roof or screened in or what?

My immediate thoughts the same as Auntthelma ... the terms and goals need to be defined specifically. If a continuously covered, attached outdoor space is the goal, I can see trouble with the existing roof lines. A practical option might be a separate, freestanding pavilion that is connected to the existing doorways by pathway awning structures. (This is the scheme used at school in Florida where we have hellacious summer rains. All the separate buildings are connected by pathways with overhead roof coverings. These are made of all types of materials (metals, fabrics, wood framing and shingles, depending on the individual circumstances.)

Sorry I didn't clarify that part. This will be just be a covered patio. Eliminating the patio door over hang. Adding the new roof extending out as indicated by my crude drawing. Coming out away from the house approximately 25' from the right side and 22' feet from the left. I hope that makes sense. We don't have a plan yet - we are waiting to see what we can come up with, as to whether it could be doable in a way that looks aesthetically pleasing to us and the budget does not make us cringe.

Yardvaark: Could you provide a picture of what you were talking about?

"We don't have a plan yet - we are waiting to see what we can come up with, as to whether it could be doable in a way that looks aesthetically pleasing to us and the budget does not make us cringe."

And that is precisely the reason you need to have a plan first! Without a well-reasoned plan that addresses all your needs, there is no way you can determine what would be aesthetically pleasing as well as budget friendly. You need to hire an architect or designer who can help you develop a plan. It is not a commitment.....it is just a far more accurate way of visualizing the potential end result

The architect is pushing for a shed roof. We don't want that - I was trying to get some general feedback about potential styles to use with this roof line

OP, you're showing us a perspective view. There's a limit to what we can understand with having only that view to look at. How wide, long and what shape/angles is it really? If we were a bird flying overhead, wouldn't the patio and house configuration be more obvious to us as to what we're looking at? Of course, it would! The PLAN view (which is like bird's-eye view) is the easiest way to understand landscape space -- its shape, size, orientation and how one part relates to the next. To START the design process, you don't need a FINISHED PLAN (though that would be the ultimate goal.) You only need a BASE PLAN, as a way to communicate to us what you have right now, before any work is done. The base plan would show the house footprint, the patio, the pergola posts and the nearby tree trunks. That's all. It is on a copy of this base plan that one would explore possibilities and be able to communicate them back to you. There's no good verbal way to do it. And because in the perspective view photo has some odd angles, it's a difficult way to do it, too. If I tried to draw the base plan for you, it's hard for me. I'd be wildly guessing about sizes, proportions and angles, so couldn't help but have a result that is inaccurate. But you're there so it's easy for you. Take a tape measure and measure the wall and patio lengths. Plot them out to scale on a piece of paper. It is literally a 20-minute process.

By the orange line you drew on the picture, are you indicating that you want to expand the patio along the back wall of the house and you wish that part to be the covered part? If it's something else, it's not clear.