Can I get an enzyme to break another enzyme down?

There is a whole class of enzymes the break down proteins called the Proteases. Since enzymes are proteins, there must be proteases that can break them down.

The enzymes are very selective from material, temp., medium, pH points of view. Thus maltase acts only on maltose, not on lactose ! beta glycosidases attack only beta  sugar linkages, in their optimum conditions ! Protein enzymes are equally selective - they ignore sugars .
But enzymes contain several bonds, including sugar & peptide links. They may get affected by other suitably acing enzymes. But our bio systems are so unique that they are very effectively isolated. Also the pH  & other factors decides the final  reactions & products .
This Q is quite thought provoking : imagine your dream enzyme starts splitting a maltase, & that maltase has ability to attack lipase under identical conditions ! - it can complicate the set up, thank God , Nature avoids this !