"I know there is a lot more involved than I am thinking."

You are right. Construction cost vary geographically. Plus the lineal footage of interior and exterior walls, doors, windows, lighting, stairs, elevators, cabinetry, fireplaces, ceiling fans, HVAC, and more are all effected. Ask your builder based upon your design. Any guess here could be fatal for you.

The first big variable is siding vs brick. Brick costs a lot more to add a foot than siding does. Then 2x6 framing costs more also (adding a foot to a 2x4 costs less). So ballparks even in the same area can be quite a bit different.

Keeping it simple, you don't need to change anything other than framing/drywall/insulation/siding/paint and then stairs. Yes, you usually change the other things but it isn't mandatory. HVAC could be a wash but that does depend on a lot of factors. Obviously wall loss goes up by 12% but if you ballpark walls as 40% then it is just 5% which may not change sizing or duct costs.

Do you know your siding cost line item? If it is brick, we can guess $100k and then just 1 foot can add 5% (from 18 feet high to 19 feet - figuring 2 feet between floors and slab construction).

So ballpark for that item is $5k.

Framing, drywall, insulation, paint would be up by probably more like 3%. So figure $200k for those and you add another $6k.

10% on stairs? So another $1k?

This is with no plan change (unrealistic), no engineering changes, and of course no window/door changes. Doors don't have to change of course but windows usually would. You could ballpark 10% on the windows since downstairs probably has larger windows. So if $50k in windows, another $5k.

So $17k for 1 foot to 1st floor only (for brick, maybe $15k for siding).

Could be twice that or 1/2 that I suspect.

This was 10 years ago, but the cost to go from 8 ft to 9 ft ceilings on both stories of our 3,000 sq ft home was only $4k. I believe the builder probably only charged us for the increased height of the wood. This was on 2x6 construction. The exterior siding was stucco and I don't think they charged us any extra for that.  The window sizes were not changed; they just adjusted the header heights.  With today's cost, I'm guessing that the same builder would charge over $10k.  As others have said, it depends on how many other things you change or affect beyond just the height of the walls.

I think it is a worthwhile "investment". I don't remember the last time I walked through a new construction with 8 ft ceilings. Most buyers expect at least 9 ft ceilings these days. Here in FL, even the cheapest production builder has 9 ft ceilings as standard.

Chispa's comment made me rethink what I posted.  I forgot that the $4k cost was only to increase the second floor to 9 foot ceilings.  The first floor ceilings were already 9 feet.  I also fully agree that it is a worthwhile investment.   I would happily pay 2 percent of the total build cost to go to 9 foot ceilings.

I know its regional but I haven't seen a house built in the last 20 years with 8 foot ceilings downstairs. And at 2800 sqft, even mid 90s houses had 9 foot ceilings downstairs.

5 years ago in our low cost of living area (prices have more than doubled since then which is new for this area) it was 5k for 1600 sq ft house. Compared to the overall price it was nothing and worth every penny.