My design takes the approach to try and use as much of the existing garage structure as possible and somehow find a way to utilize this and incorporate into the new design. This will save on the budget and allow you to do other work.
I did a little research for your area and it seems the zoning for R10 in Arlington requires a min 8 feet side yard with an aggregate of 16. I could be mistaken, but if so you will need a variance to construct a new garage within the setback. I was hoping that even if you extend the existing side wall toward the back, by keeping the existing left side wall you would be pretty close to 8 feet from the side property line at that point.
I also feel the garage being square to the house will look better and give more options to incorporate the new design into the existing façade.
I think if you raise the existing garage slab up about 12/18 inches it should be very close or just below the first floor line of the house. You could perhaps salvage the existing slab and simply install new metal joists right on the slab, and then pour a new lightweight gypcrete slab on top. The new driveway could be installed to the new higher level. This would be better also so the driveway is not sloping down as much. This would also save on demolition costs.
[It might even be possible to raise the new garage floor even higher, at about 18/30 inches so the new finished garage floor would actually be above the first floor. You could then cantilever the new slab overtop the first floor for a few feet so no structure would be required below.]
Then if you remove part of the front wall of the house you could create extra depth for the new garage. Assuming the new slab was just below the first floor, the top of the existing foundation wall would act as a curb to stop the car tires, and the nose of the car would project past and above the existing floor beyond. This would require no structural changes to the interior of the house either above or below this new opening. It would merely be a “niche” facing into the garage that would give you an extra few feet of space.
In my design I kept most of the left wall and the corner to limit the amount of demolition. A new beam creating the opening could rest at the corner. Then the new garage could be extended toward the rear to line up with the existing porch. This would give you a lot of extra storage room inside the garage.
I then utilized the remainder of the office as a large mud room and storage area. This could take the form of built-in cabinets, benches and counters. I kept the existing closet and closed off the remainder from the entry area, then added a new side door to the garage. The existing door from the office would remain as the exit from the garage to the porch beyond.
With hopefully the savings in demolition and new construction of the garage, you could add a new office to the front of the house. I then added a new entry vestibule to provide access to the new office. As a design element this will add curb appeal to the front. To integrate the design into the existing front, I set the roof planes of each part at different heights. The new office in the center has the highest and will allow nice tall ceilings there which also provides for a dramatic tall glass wall.
You might even be able to repurpose the existing stone as the base of part of this new front. To keep the house as open as possible I provide a new taller door with sidelights of the same width. The entry and office are set at one step down from the existing floor to minimize the steps up to the front door so the landscaping is integrated with the new addition.
For your requested alternate scheme I thought t made sense to take advantage of the nice views possible from a rooftop deck. If you are thinking of extending a tower up to access the roof I propose actually locating the new space there.
I was also pleased with the alterations to the front and was inclined not to extend those additions any taller to create second floor space. I felt adding more density to the façade would not be aesthetically pleasing.
So my solution was to extend the new rear area of the garage up to a new second floor space. This enabled me to design it in a way to be recessive and compliment the new front design. I located a new bath and closet here to be a new en-suite to serve the end bedroom. I then converted the existing en-suite bath to a new laundry. These changes should be relatively cost-effective. The existing plumbing stacks should easily serve all the changes. By doing this, you could open up the existing laundry area to the second floor hall overlooking the entry below to make the space more expansive. From this new space a stair could lead up to a new rooftop structure.
This new structure would extend the existing façade essentially to a new third floor, which would add a dramatic new profile to the front façade. I would extend new masonry up the face to match the existing, then for structural reasons, wrap the remainder in wood siding. Ribbon or clerestory windows could wrap all four sides, along with glass doors to a new roof deck.
I propose a structure large enough to accommodate a full bath (right on top of the existing second floor bath) and an open lounge/office area with glass walls. Since I presume the best views are to the north east toward the Potomac where the rear roof area is taller, I provided a new deck directly off the new space which then has steps up to an upper deck at the rear. I wrapped the entire perimeter with horizontal metal railings.