Talk to your local building department -- city/town/county.

It varies from town to town. In our town, the square ft. limit is 1.5 times the buildable area, (which is lot size minus setbacks) Second story included.
Check with your local building department or where you would go for permits.

Yes, it is common for both zoning and home owner associations to have a "maximum buildable area" as part of their development standards. Check with your zoning administrator or HOA, as appropriate.

Check how the square footage is to be calculated.

Our town has FAR (floor area ratio) requirements. This is about *bulk*, not just 'spread'.

If you're close a variance may be an option. Ask about that. But get the rules and do the math yourself. Some things may not count.

Some properties are subject to home footprint and/or overall size limitations due to either architectural covenants or zoning restrictions. If applicable, these should be referred to in the deed for your property that is recorded at your municipality's courthouse.

The restriction is usually in the town's zoning ordinance. As noted above it, can be either a Lot Coverage limit (gross footprint area/lot area) or a Floor Area Ratio limit (FAR) (gross area of all floors/lot area). Its a pain to calculate because a garage or porch or walk out basement, etc. might be included or excluded from the gross area calculation.

The limitation numbers are often listed in a zoning ordinance chart of residential zoning districts so you must start with a zoning map and find the code for your district. These rules are usually enforced by the local building department so you could save a lot of time by going there and asking for help.

When we bought the lot for our last house, there were pegs marking the boundaries of the lot, and another set marking the building envelope - the area within which the house had to be built. There were also height restrictions, which caused our architect some angst because the house was on a slope, so the height from ground to roof on the lower side was pushing the legal limit.

Fortunately, height is not expected to be an issue and yards/setbacks would only be an issue if the existing house was currently nonconforming. I often get asked to determine the zoning limits on an existing house. Did it 6 times for an old friend's son last month. It takes about an hour on the internet if I have an accurate survey otherwise I'm forced to guess or field measure to fences which is not reliable.

The difficulty these days is limits on impervious surfaces and the engineering required to meet drainage requirements for large additions. That would not be an issue for a second floor.

Height limits are usually taken from the average grade around the house and since a survey is required for an addition, the surveyor can do it but I always check the numbers..

"This addition would only be a second story. So the height limit is not a factor."

I can only take the OP's word for it but if she were a client I would ask for an up to date survey with all the necessary information on it.

I suspect it hasn't even been looked into...just my opinion though. Most people have no idea what restrictions there are for additions/building. The fact that the OP doesn't know if they've maxed out square footage makes me think, and I obviously could be wrong as you know what they say about assumptions, but I do think none of the rules have been looked into.

The best thing the OP can do is go visit the office of the local zoning administrator and find out what is and isn't allowed on the subject property.

Height limits are usually taken from the average grade around the house

In some municipalities I have built in, including my latest build, height is determined from the crown of the road.

The reason its OK to think that the height limit will not an issue is, if the house is on a relatively flat lot, the height restriction is usually for 2 stories and some reasonable dimension limit that would allow a second story plus a sloped roof. so the OP would simply build to that limit. As for other limitations, many towns don't have an FAR limit. I built a house n VT and the inspector only wanted to know how far it was from the road.

If the OP told me the town, I could figure it out pretty quickly but, as I said before, its easier to go ask the building department but I guess it deserves repeating a few times.

Perhaps I've missed something, but I thought the issue was floor area ratio, and how much buildable area was allowed on the property. What does that have to do with height limits?

As the OP posted, "... So the height limit is not a factor..."

Where I live, it's pretty easy to look up the relevant regulations on the local council's website. I'd start there, then head down to the planning office for more detail. Rules about what is or is not permissible vary enormously from city to city, never mind state to state or country to country. And beyond the question of building envelope, there are other planning criteria you may need to be aware of. As an example, we were required to install sprinklers on the roof of our last house, have a rainwater tank under the house, and a pump to pump the water to the roof. That was strictly a local requirement, obviously, and one we weren't aware of until the council insisted on an okay from the local fire department.

58% is generous. What is your lot size?

Study the definition of "Gross Floor Area" and "living space" or "habitable space" in the definition chapter of the zoning ordinance. GFA rarely includes a basement unless its more than half way out of the ground or based on an average of the exposed sides, etc. Sometimes mechanical space is excluded.

The rules for gross floor area vary greatly from town to town and often change as the towns try to stay ahead of developers. There are sometimes credits for larger setbacks or bonuses for small lots, etc. Carefully read the actual text of the ordinance.

Post a link to the ordinance if you can.

"...It turns out that max square footage of livable space (including basement and garage) for our zone per city code is 0.58% of entire lot size. We are right up on the max! Drat! So we can’t build on..."

Jen, click on my name and send me a private message. There's too much of an echo in here. Do it soon; I'm not going to be here much longer.