We revisit our rope model for string fragmentation that has been shown to give a reasonable description of strangeness and baryon enhancement in high-multiplicity pp events at the LHC. A key feature of the model is that the enhancement is driven by the increased string tension due to strings overlapping in dense systems. By introducing an improved space–time picture for the overlap between fragmenting strings, where also non-parallel strings are properly taken into account, we are now able to investigate the enhancement both in jets and in the underlying event in a consistent way.