Possible Clues:

• Increase rapidly or go down the tube?
• Step up, as a conflict
• Rocket, key one, behind time
• Intensify destruction of a celesta
• Heat up
• Build up new case, behind schedule
• Bring up sharply key note about a US city
• Climb a castle, destroyed after end of siege
• Breakup box behind schedule and it will go through the roof
• You are in Rome, caught with a dead mushroom