Basic would be around $50-75 depending on area of the country, finishes, # of windows, etc.

Design a small one story house. Price out the foundation and roof. Now price out the kitchen and bathrooms. Now price out your HVAC for the first floor. Basically build a small house which has all of the essentials. Now calculate the additional material cost of doubling the square footage and factor in the added labor of getting that material to the 2nd floor, a cost that wasn't incurred in building the envelope for the first floor.

You see, a gross dollar figure includes the high expense items like kitchens, baths, furnaces, air conditioners as well as foundation and roof. That $100 a square foot is an average, not an actual cost per square foot for each marginal square foot added. If you expanded a ranch house you could piggy back on the systems and features in the house already and your cost would be less than, say, $100, but you'd still have to pour a foundation and build a roof. The same goes with a 2nd floor, minus the new roof and foundation but with higher labor costs.

The point here is that, to the best of my knowledge, there is no general rule of thumb because the proportion of cost that goes to roof, foundation, kitchen, HVAC, baths, etc is all over the map depending on individual houses. I would think that if you really want to get an answer that is somewhat accurate for your purposes you first need to do the above - design a house that interests you, cost it out to the best of your ability, and then you can extrapolate the labor and material costs, as well as the marginal cost increase for beefing up your HVAC and plumbing and electrical that come with expanding square footage for the second floor.

Alternatively, for a quick and dirty answer find the proportion of cost that is assigned to kitchens, baths, foundations, roof, etc and then the remainder is what you have for framing, drywall, etc, the parts of construction that are most closely associated with square footage.

You could have a really cheap 2nd floor if the floor was one big loft with no plumbing up there and no windows and doors. The cost would increase if you started adding a steam room, a fireplace, a master bathroom, a private deck for the master suite, etc. If you want cheap space you can get really cheap space by putting no frills up on the 2nd.

This is why the typical answer to your question is "it depends." It really does.

s.f. cost numbers should not be used to estimate the cost of a building; they are only broad general indicators even in the hands of an experienced professional. Such numbers are generated by totaling the costs of a specific building and dividing that by it's floor area. Trying to work in the other direction is almost always misleading because there are far too many variables in the design of a house.

In general the use of simplified rules of thumb can only get you into trouble unless you have a well written database of many projects you have actually built and plan to build again. Even then it would be very difficult to determine the cost/s.f. of one floor separate from the one below it.

"I know the price is higher for square footage on the first floor"

Square foot pricing is not reliable for much of anything (except large commercial work).

The variation in cost per square foot even in a single house distorts any attempts to use it reliably and accurately.

There are certain fixed costs like electric, plumbing, bathrooms, and kitchens that are very expensive on a per square foot basis.
Living rooms, dining rooms, foyers, family rooms, etc. then appear inexpensive.
They 'share' the fixed costs over a larger area.

Adding a second floor is going to impact some fixed items (higher HVAC capacity) but do you want empty space?
Bedrooms?
Bathrooms?
If you are on septic every bedroom impacts tank and field size, but does not affect DWV on sewer much.
It can affect water meter and line size.

You would do much better to decide what you want and need, and then look at costs and adjust than try to use square foot costs.
Insurance companies normally have enough loss to then use average costs in setting policy costs, but they know that it is an average.

The first step in comparing the cost of 2 complex things is to carefully define what they are and then compare their costs item by item in a spreadsheet. I'm not sure that is even possible for what is suggested but comparing general s.f. costs ignores that principle and therefore the results should be considered at best worthless and at worst misleading.

Rather than trying to invent your own design and construction guidelines talk to someone who has been doing this for a living for a long time and possibly save yourself a lot of time and money.