Current models of class II methanol masers are able to describe the brightnesses of the strongest masers and provide a basis for explaining observed line ratios. Determination of the physical parameters in the source requires observational data in many maser transitions. In order to provide observational constraints for models we searched for and detected 7 new methanol masers. This allowed us to constrain the physical parameters of the 3 sources with the greatest number of detected methanol maser lines: W3(OH), NGC6334F, and G345.01 + 1.79. The models accurately account for the fluxes of the bulk of the detected maser lines. Remaining discrepancies most probably reflect the fact that the most prominent components of the different maser lines are formed under different conditions. This is supported by comparison of the line profiles. We outline directions for future studies in the field.