The phrase "make higher" typically refers to increasing something in its height or elevation. However, there are a variety of synonyms that can be used instead of this phrase to convey the same meaning. Some possible alternatives include elevate, raise, lift, boost, escalate, enhance, augment, amplify, and raise up. Each of these verbs suggests an action that makes something taller or more prominent, whether that be physically or metaphorically. By selecting the most appropriate synonym, writers can add variety to their language and create more vivid descriptions that engage their readers' imaginations.