The phrase "visit on" can be replaced with several synonyms, including "impose," "inflict," "bestow," or "confer." Each of these terms has a slightly different connotation or context. "Impose" implies a sense of obligation or burden, as in "he imposed his presence on us." "Inflict" suggests harm or unpleasantness, as in "the storm inflicted damage on the town." "Bestow" implies a gift or honor, as in "she bestowed her blessings on the newlyweds." And "confer" suggests an granting of authority or recognition, as in "the committee will confer the award on the winner." Choosing the right synonym can add nuance and depth to your writing.