Based on what I've read, I think this is correct (and there is no way Vivek would have gotten to this point if there was no way to construct the desired improvements that didn't involve replacing the existing structure - that's just not happening).
Having no specific knowledge about the site or existing structure foundations (and some quick Googling and looking at Google Earth photos over time didn't really help), there are often ways to retrofit a building to enable additional foundation loading capacity. Structure foundations are kind of my thing.
If they are adding foundation capacity
outside of the current building footprint, they can use one of several kinds of pile foundation types (CIDH piles, auger cast piles, etc.) - but probably not driven piles since the vibrations would not be good for the adjacent structure(s). Still, they have plenty of options that have been used all the time in the Sacramento area (CIDH [cast-in-drilled-hole] foundations are used for many bridges, for example, and the Golden 1 Center is supported on auger-cast piles, as are numerous other tall structures downtown - the company I work for has helped design foundations for several of them).
If they have to work
within the existing building footprint, or will underpin the existing foundation perimeter, they have a few options as well. One frequently used method is micropiles, which were used to underpin the Bellagio hotel in Las Vegas, for example. Another might be helical anchors, which are often used for foundation underpinning applications. There are probably a few others as well.
So yes, foundation capacity can typically be increased, if necessary.
Now, that's assuming that the foundations are the issue. When they say "expanded", they issues may be due to above-ground structural limitations and not foundation capacity. The axial (or lateral!) capacities of the columns, beams, shear walls, trusses, their connections, or other items may not be sufficient to support another level of loading on top of the existing structure (or for a retrofit/remodel of some kind). That's a bit outside my specialty area so I'm not going to elaborate on this too much. But structural engineering firms have been helping out with structure retrofits for additional seismic loads (or other loading capacity) for what, 40+ years? (There was a statewide push for bridge seismic retrofits in the 80's, for example, and updated building codes over decades have required structure upgrades during remodels, etc.) I'm sure they can figure something out, if necessary.