That's not an A-frame, It's a glass-ended house with a steep gable roof.
This is an A-frame:
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The things are _all_ roof, no side walls.
If the structural engineer says it's OK then it is. But you need professional design input to alter the structure that significantly.
Casey

I apologize for my misinformation. Clearly I am not very knowledgeable in my terminology.
This would certainly not be a do-it-yourself project for us. If we got to the point of drawing up plans, we will involve a contractor. We live very far out of town, though, and I haven't wanted to ask contractors to come out to quote two different options on a project that likely won't happen for another year or two.
We have been told that the roofing cost will be high because of the pitch. That is why I was wondering if the lesser roofing cost associated with the pitch of new dormers would help to offset the framing costs. I wasn't looking for specifics but simply an idea of how these would compare.
Thanks for your input.

Great looking house, beautiful setting! I think it would be more economical - and much more satisfactory - to add on at the back of the house than to build dormers to expand the loft.

The things to be studied and factored in: how is the roof framed? Load-bearing ridge? Timber framing with purlins? How is the floor framed, as you will be extending the loaded area of floor out to the wall plates? Are the joists OK with the extra sq ft of loading? Kinds of questions a PE and architect will answer.
Foundation work on an footprint expansion is usually expensive enough to make an upward expansion the more economical choice, even factoring in significant structural costs.
I don't want to discourage you in the least; it looks like a cool project.
Casey

Re roofing and adding a dormer is apples to oranges.

Figure out what you'd like to do dormer wise and get a price on that.

If you decide to do the dormer do it before re roofing

Then get a price on a re roofing.

Don't be surprised to find it a higher price since you've complicated the job.

Hello! We have very similar homes. Here in North Carolina it's called a chalet style home. We just bought ours -- it was built in 1988 and still has the original roof (and carpet and everything else) -- the roof will be the first thing changed -- hopefully starting next week. We are just "chopping off the chimney" at the roof line since the fireplace was replaced with gas logs -- and that added about $4000 to our roofing cost. So, I'm sure that adding the dormers will be quite an add-on.

Thanks for all of your input! Readyami, would you be willing to share the square footage of your home and the cost to redo the roof? And thanks for the name clarification. Chalet style- I like it.

I might start specializing in chimney chopping.

Right, Mag77?
Treadingwater, our house is 2200 sf, but it's not "apples to apples" with yours because the steeply-pitched part only covers half of the house. The front half is the steep pitch, and back half (which houses the full-sized rooms on the second floor behind the loft) is a more normal pitch. The quote was more than we were expecting, but was consistent across several quotes. $12.5k including our contractor's fee.

Place a level against the roof.

From the point where the level touches the roof, measure out 12 inches.

From this point measure the distance in inches from the bottom of the level to the roof.

This will be the first number in the roof pitch. The second number will always be 12.
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Or you could use a Roof Pitch Calculator or an Angle Finder.

Most houses today run between a 4/12 to a 8/12 pitch. Since your roof is much steeper I just listed degree for pitches ranging from 12 up to 24.

12/12 = 45ð Degree angle.
14/12 = 49.4
16/12 = 53.1
18/12 = 56.3
20/12 = 59.0
22/12 = 61.4
24/12 = 63.4

This kind of roof requires a structural ridge beam because there are no horizontal ties between the wall top plates. Adding large shed dormers may increase the load on the ridge beam which might not meet he current code for strength. The same might be true of the rafters which might be stress-skin prefabricated plywood panels.

The first consideration for this kind of project is to hire an engineer to inspect the structure and determine the structural design requirements. The difference in the cost of roofing will be of little or no importance.