Based on a common attribute, the FeatureJoiner (before 2018 FeatureMerger) can do this.
Based on Spatial interaction, this can be done by the Overlayer transformers or the NeighborFinder.
Many options to transfer attributes, based on joining (merging) data.
Most of these have the options to merge Geometry/Attributes only/Both.
Based on a common attribute, the FeatureJoiner (before 2018 FeatureMerger) can do this.
Based on Spatial interaction, this can be done by the Overlayer transformers or the NeighborFinder.
Many options to transfer attributes, based on joining (merging) data.
Most of these have the options to merge Geometry/Attributes only/Both.
Thanks @erik_jan! The Overlayer transformers are what I needed.