The antonyms for the phrase "more under-the-counter" can include open, transparent, lawful, legitimate, authorized, official, above-board, and visible. These words indicate a clear and legal process rather than one that is hidden or done in secret. When something is described as "under-the-counter," it implies that it is being done or sold illicitly, which is why its antonyms suggest a lawful and legitimate approach. By using words that convey legal and accepted practices, one can avoid the negative connotations of "under-the-counter" and present an image of trustworthiness and legality.