By "continuous light" I guess you mean a tungsten kit with fresnel lights. You can make a fresnel light into a soft light by placing diffusion such as 1/2 or full grid out in front, or else by placing a chimera on the light. You can never make a flo light into a fresnel light. Fluorescents are soft light tubes and cannot be focused.
For interviews, so much depends on the style you like. My personal preference would be to have a soft key, a piece of 4x4 foamcore to bounce the key into the fill side to taste, and a second soft light for a back light. For my 3rd light I'd like a fresnel light to put a splash of "sunlight" on the chest of the subject, when it's appropriate. Then I'd like 2-3 more lights, at least one of which would be fresnel, to handle the background.
Bottom line: I could work with either a complete set of fluorescents such as Kino Flos, plus 2 650 or 1K fresnel units, or else all fresnel tungsten units with some diffusion as needed.
If expense were no issue, I'd have a complete daylight set of lights, including some 1200 HMIs fresnels, some kinos bulbed daylight, etc. and some jokers. Why? Because 90% of interviews seem to be in rooms with daylight and/or existing cool-white fluorescents. If all I could afford was tungsten, I'd be sure to have plenty of 1/2 CTB gels. I'd also have minus-green and plus green to balance to green spikes in existing lights. See my post about the blue-red axis and the magenta-green axis on the thread, "a little bit of green."
And if any of the above is too expensive, start with just a flexfill to bounce some existing light into the eyes. If you look carefully at the location, you can almost always find a way to shoot with existing light plus some bounce. If you look carefully, you can also usually find a better available-light location in or near the same place, though then you have to be able to persuade your interviewee to move to that location.