There are various synonyms for the phrase "enjoy a modest competence," which refers to a state of having moderate or satisfactory skills or abilities. Some of the synonyms include "possess a moderate proficiency," "have a decent aptitude," "be reasonably skilled," "attain a satisfactory level," "be adequately competent," "achieve a modest mastery," "attain a moderate level of expertise," "have a satisfactory command," "reach a reasonable level of competency," and "have a modest ability." These synonyms can be used interchangeably to describe a person's proficiency in a particular area, such as a skill, knowledge, or ability.