Answer: Feverfew, or Tanacetum parthenium, can be deadheaded to try to encourage more blooms. Most gardener will at least shear off the plants to try to prevent it from self seeding because it can be somewhat prolific in that way.
Best blooming performance will occur where there is ample moisture and the soil is rich. When you trim it back, if you wish to do it flower by flower, cut just above a branch or leaf stem taking care not to damage or remove the remaining flower buds. Otherwise, after the main flush of blooms has faded, a general overall "haircut" to remove the spent blooms will do.
The other plant often called feverfew, Parthenium integrifolium, can also be deadheaded to enhance blooming and tidy things up. On this plant, remove the faded blooms by cutting off the top portion of the stem, leaving lower branching portions intact to bloom later and leaving the basal foliage in place.
On both plants, trim away the stems and foliage in late fall after frost has killed them back.
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