Zoning is not usually a constraint. But math and geometry are.
The above is a screenshot of UrbanForm's Filter function, filtering for all sites in Portland that allow housing.
As you can see, the vast majority of sites are zoned to allow housing uses, including the main high-rise/office districts of downtown, Pearl, and Lloyd District.
187,355 lots out of a total of 196,734 means 95% of the lots in Portland allow housing. Pretty much everywhere except heavy industrial zones and areas designated for parks and open space.
So zoning is not typically a constraint when talking about converting existing office buildings into residential buildings.
However, math and geometry are constraints. Or, to be more specific, the finances and the technical and spatial considerations are often the major obstacles to converting offices to residential.
The NYTimes recently wrote a great article that goes fairly deep into why certain spatial factors make only a limited kind of office building a good candidate for converting into residences.
In short, it has to do with distances from windows. Many office buildings have really large floorplates, and bedrooms and living spaces are required to have access to fresh air and light. This is not just required by building code, but it's also good architectural practice, to say nothing of market reality--try selling a living room with no access to natural daylight on the open market.
The large floor plates of typical office buildings make spaces farthest from windows practically unusable in a residential use-case without significant modification.
The best office floorplates for conversion are typically older, pre-war buildings that did not rely on the modern technological advancements of artificial lighting and air-conditioning to make spaces farther from windows habitable.
But even if an office building has a basic configuration amenable to conversion into residences, the next hurdle is financial.
Simply put, it costs more to design, plan, and build within an existing structure than it does to build from scratch.
In converting an existing office building into something new, you are constrained by existing means of access and egress, limiting the quantity and increasing the time and cost of moving labor and materials.
Residences require many more plumbing fixtures than offices. Think of all the kitchens and bathrooms required for an apartment, compared to the centralized bathrooms of office buildings. This is a lot of plumbing work and coordination into the existing structure.
Cutting up the large open areas desired by many offices into the many rooms of an residential units mean lots of air movement will have to be managed. This means ducts for heating, ventilation, and cooling, as well as the distributed equipment that is necessary for the finer level of control required for residential spaces.
And then, new structural codes sometimes require significant structural upgrades when you are changing from office to residential.
In sum, the constraints for converting office to residential are spatial and financial. Not usually zoning.
The spatial constraints cannot be changed, since the whole point is using existing buildings with their existing spatial limitations. The financial side, for any builder, will be whether or not they can make money from the increased burden of working within the spatial constraints of existing buildings.
With the increased desirability of living outside of high-rise, extremely dense city centers, there will always be the option for a builder to simply build where land is available without an existing building.
For jurisdictions that want to promote these kinds of conversions, then, there is only one thing they can do: make the financial side of converting pencil out.