All-fiber Raman lasers have demonstrated their potential for efficient conversion of highly multimode pump beams into high-quality Stokes beams. However, the modal content of these beams has not yet been investigated. In this work, based on a mode decomposition technique, we are able to reveal the details of intermodal interactions in the different operation regimes of continuous wave multimode graded-index fiber Raman lasers. We observed that, above the laser threshold, the residual pump beam is strongly depleted in its transverse modes with principal quantum number below 10. However, the generated Stokes signal beam mainly consists of the fundamental mode, but higher-order modes are also present, albeit with exponentially decreasing population.