would be helpful if the photos actually attached...

Photo #2...

You need a pro here playing with a lot of valleys in a roof creates many problems with how to take care of rain and snow.

so is that blue-grey gable shown in the rear of your first photo your house too? if so... i'd consider it possible... to extend a portion of that roof line towards your corner where your doors are, overtaking your existing garage roof in that section, your awning structure over the door, and the roof above that. simplify rather than complicate.

but i'd need a more complete photo of your whole house to see if that would work.

@ninigret - no, that gable you see over the garage is the neighbors house. I’ll find a better picture to show my house. The roof line of my house has a single ridge running perpendicular to the garage roof ridge shown in the picture above.

@beverly - thanks for the mock-up and suggestion. Maybe that’s all we need, and it would be a smaller/simpler project than taking it right up to the house roof line.

Might be possible to then add a window above the extended entry roof and below the main house roof to get more light into the entryway

Here’s a wider shot that shows the house roof a little better

Seems like you could extend the main roofline forward to create a 1.5-story foyer...no?

Rather than extending the upper roof, I would do a separate gable over the new entry, below the existing main house roof, parallel to the garage gable .
Since you live were it snows, this would keep snow from sliding off over the entry.

I think it would look better, as well as being a simpler roof to tie in framing wise to the garage roof. Of course you would need a cricket where the two gables meet, but it would not show from below.
I don't know how to do photo shop, so no help with what I am envisioning, maybe someone else does...

@course411 - yeah, that’s our initial thought

@cookncarpenter - thanks, that’s an idea we hadn’t considered

I've never seen an attached garage that wasn't accessible from inside, so I suspect the house has been remodeled and a door to the garage closed off. Whether or not that's the case, it might be easier to get interior access to the garage by working within the house.

If it turns out you do need to build a small vestibule, keep it simple. It's easy to think about soaring gables and sweeping eave extensions, but they don't make financial sense.

The existing roof over the front door begins under the third row of siding down from the soffit above it. If it began under the first row, it would extend twice as far. That's enough to let you easily build a 6 x 6 vestibule, maybe 7 x 7 with a little tweaking. No major changes to the roof. The same simple gutter configuration.

@skil - thanks, that’s great advice.

I agree that it’s an unusual configuration to have no interior access to the attached garage but in this case it is actually the original design.

skil: Our 2 car garage is attached but does not have an interior access to our house, designed that way. We have a Garrison Colonial. The garage is attached to the house for about 2/3 of its length. Then there is a covered porch with a door to the garage and a door into the houses. We have a lower home insurance rate because a thief or vandal cannot enter our house directly from the garage. Apparently garages are easier to breach and, once inside the garage, the thief can take his time working on the door to enter the house.