Check the city's zoning strategy. Some cities allow different zones in a small area or along the same street. Many group them, such that all single family homes are on A, B and C street, and duplexes on D street and four-plexes on E street and 6-plexes and higher on E street.
First, phone the city planning department. Assuming the city generally would support a re-zoning, you will then submit an application with appropriate documentation for city council to consider it. The planning department will make a recommendation such as "forget about it" or "we approve it" or "we approve it with conditions".
The biggest issue you may encounter is:
a) parking requirements
b) adherence to current building code, such as fire code, setbacks, window sizes, roof slope, railings, eaves, electric wiring, etc.
The cost to bring an older asset into compliance may be minimal but are often quite substantial.
The associated documentation is a survey of the property and an engineer's report confirming conformance to current code (after a lengthy renovation phase perhaps)
You also will have to consider if you wish one title with 4 units on it, or 4 condos that you could sell individually.
Its a fairly straightforward and easy process, but the cost may be prohibitive. Phone the city and you will find out with a few phone calls if it is worth it.