I read that a "Doctor of Science" is awarded for research well beyond a usual PhD degree awarded for a dissertation work and includes a portfolio of high quality papers in interdisciplinary fields. Does this mean that one cannot actively pursue this degree and one can never be certain of how close one has come to a DSc? How does career planning at such a stage look like?
I own a PhD, but it is the first time I've heard of "Doctor of Science". In the former Warsaw pact countries and some Western European countries there are two level of doctorate. First is the "canonical" PhD and second is called something like "habilitation" which allows you to have PhD students and conduct your teaching in an independent manner.
I see two reasons you asked the question:
in your country, for a certain reason (for example, having own PhD students) you require this title. In this case, ask your Department of Education what are the exact requirements for this. If they legally require such a title, they also provide a clear path to get it.
you look for a title. Simple put, the simplest approach in this case would be to identify universities offering this title, join a program and earn it.
The way you asked the question makes me thing you fall in the second bucket. Probably the following story will help you rethink your course of action: Legend has it that one of the founding fathers of Shotokan Karate-do is asking a student at a seminar what is her most ardent desire. The student replies that she wants to have the black belt. The master replied that he can easily confer the black belt, but would that make her a better karateka?
The meaning of a DSc degree almost certainly varies by country. In my experience in the commonwealth (i.e. UK, Australia, New Zealand) it is an honorary degree. That means you don't "pursue" it; it isn't attained by being a student. It's more of a "lifetime achievement award" -- you get it as a result of a long and successful career in science. The usual course is that you get a PhD first, then become a Lecturer/Professor, and after, say, 20 years, if your research track record is sufficiently outstanding you apply/are nominated for one and get awarded it as a special guest at the graduation ceremony (usually from the same university that gave you your PhD).
The meaning of a "doctor of science" degree definitely varies by country.
For instance, the standard degree in Germany depends upon what kind of program one studies. As an example, the doctorate for natural science is normally "Dr. rer. nat." (Latin for "doctor of science") while engineers get Dr.-Ing. degrees, and an engineer could not apply for Dr. rer. nat. Either could get a Ph.D.
In the US, fewer schools offer the Sc.D. At MIT, the two degrees are interchangeable, but at other schools there may be slight differences, although there is no expectation of significantly more work.