In a method and apparatus for recording a magnetic resonance data set, an MR data acquisition scanner is operated to acquire a range of basic values of a material parameter of a subject, with a basic resolution within a region of the subject. Thereafter, the aforementioned resolution is refined by selecting a refinement acquisition sequence, dependent on a material property to be refined, and then again operating the scanner to acquire further values for the refinement material parameter with a refined resolution, compared to the original resolution.