Two problems surface immediately, but are not insurmountable.
One the columns (at least at the ground level) will see their basic loads increase in approximate proportion to the number of levels added. These members may or may not have sufficient existing capacity. If they do not, they can be improved. One of my favourites is to encase a concrete column with a steel box slightly larger than the old section and grout the gap. If it is a steel frame, one can easily slap reinforcing plates on the old section. The existing floors plates see no new load, so they are likely good to go.
The other problem is the substructure and knowing what capacity you can derive from the foundation and the soil system. If you are on any kind of semi-reliable rock, you will be in better shape than if you are on wet clays, etc. Again, we can improve substructure capacities in many ways, but they are not always cheap.
If you can get a grip on those to aspects then adding floors is a snap! Make sure you have enough room to get men and materials onto the site without disturbing adjacent properties (including any excavations and back-slopes).
Unless the structure becomes significantly taller, then I doubt that you will encounter any dramatic problems with overall structure behaviour. The biggest question mark might be the particular soil-structure interaction for your given local seismic characteristics.
Member of the SSPIA Senior Committee. Have a question? Go pester Tony.