Asking after someone's well-being is an act of kindness that shows one cares. Depending on the context, there are several synonyms that can be used as alternatives to the phrase "ask after." "Inquire about" or "check on" can be used to ask about an individual's health or status. To show concern for someone's progress, "follow up on" or "keep tabs on" can be used. In a more formal setting, "request an update on" can be utilized. Overall, using a synonym for "ask after" can help diversify one's vocabulary and make conversations more engaging and interesting.