The term BOOST WITH UP can be broken down into three crossword solutions: AMP, REV, and LEG. AMP stands for Amplifier, which is an electronic device used to increase the strength of a signal. REV stands for Revive, which means to bring back to life or restore to a former condition. Finally, LEG stands for LEG Up, which is an expression meaning to give someone an advantage or help them out. All three of these terms are related to the idea of boosting something with an up, whether it be a signal, a condition, or an advantage.