@Alyssandria L.
We ended up passing on the home because of a home inspection that revealed not only a considerable amount of deferred maintenance, but also issues with the foundation, electrical that would've required major expenses that no longer made the numbers work for us. The big lesson learned from it all: If you're serious about buying a short sale, have it inspected before bank approval; even knowing that the bank might reject your offer and you'll be out $400-$700. It's better than waiting for 4 months like we did only to find out the property was horribly maintained.
Now, regarding your question: Before we did the home inspection, we demanded that the seller's agent get the zoning certificate re-certified for a 3-unit building; as we had no doubt that it was built pre-1957 zoning ordinance. She presented her case to the zoning board and then they recognized the coach house as the third dwelling unit on the RS-3 zoning cert. I was a bit surprised at how easy she was able to accomplish this. I'm not sure if they used water records or building records to prove it was built/existing pre-1957. Is your property of interest being marketed as 3 unit? Only the zoning certificate will show how many legal units are recognized on your property of interest.
In your case, you may have difficulty getting any additional unit legally recognized, or even 2 units legally recognized, unless they were pre-existing to begin with and built before the zoning ordinance was put into effect in 1957. Adding additional units that were never there originally probably won't fly when it comes to getting them legally recognized by the zoning board. I can't say it's impossible as I'm not professionally qualified to answer; it's just based on my understanding of the process.
Note this section in the zoning ordinance:
A pre-ordinance (built before July 8, 1957) residential building or building of mixed residential occupancy not complying with the requirements in force and applicable to the building at the time of its conversion may, if permitted by the Zoning Ordinance, be altered so as to legalize the present number of dwelling units provided such building complies with all the provisions of Chapter 13-196. For conversions which have added only one additional dwelling unit over the original number permitted, the provisions of Section 13-196-740 shall apply.
Other things to consider:
1) Is the basement unit you plan to finish at least 7.5 feet high? If it isn't you'll never be able to get it legally recognized by building department even if zoning allowed for an additional unit.
2) If you do successfully convert to a legal 5-unit property, if/when you eventually sell that property, you will disqualify your typical buyer pool that is approved for taking on residential mortgages as any property with 5 or more units is considered a commercial property. This will greatly reduce the pool of buyers as commercial loans are more strict and require higher down payments.
3) If you choose to buy it as a 3-flat and choose add an illegal 4th unit, I suppose you could owner-occupy that unit it to reduce the risk of the city finding out. I have heard of many house-hackers that do this when they live in the illegal in-law unit in the basement and rent out the other legal units.
I would make sure your investment works with the way the building is currently zoned versus how it would work with hypothetical units added to it. Good luck!