The phrase "enjoy great favour" can be replaced with numerous synonyms, each with their own subtle differences in meaning. Some common options include "bask in popularity," "revel in admiration," "delight in approval," and "cherish respect." Other possibilities might include "savor adulation," "thrive on acclaim," or "take pleasure in esteem." Each of these synonyms conveys a sense of experiencing positive attention or praise from others, but the nuances of their meanings can help to express different nuances of emotion or context. Ultimately, choosing the best synonym will depend on the desired effect of the sentence and the tone of the surrounding language.