When talking about the opposite meaning of "more near-at-hand," one can use phrases like "further away" or "distant." Other antonyms for this phrase include "far away," "remote," "inaccessible," and "out of reach." These terms suggest a distance or gap between two objects or locations. They also imply that something is difficult to access or approach, either physically or in terms of time or effort required. Conversely, "more near-at-hand" implies that something is close, within easy reach or readily accessible. Ultimately, the choice of antonym depends on the context and individual nuances of the situation at hand.