How to break a system built on power over others?

There are four basic approaches you can use: absorption, infiltration, attack, and disregard.

Absorption approaches a system from above; it means you're already above the top of that system and descend to manage it more closely.

Common examples for the absorption approach are outright buying out a system or otherwise acquiring it without any resistance.

Infiltration approaches a system from below; it means you start as a powerless peon and work your way up the ladder to greater power. Once you have the power, you may make changes to the system for your own goals.

Typical examples are careers in military and corporate systems.

Attack approaches a system from the side; the system under your control is similar in structure and purpose to the target system, and you use any means in the context of the operation of these systems to exert control over the target system.

Typical examples are classical states at war and competing businesses.

Disregard doesn't approach the system at all. How can it control or break a system then?

Disregard works by (intentionally or unintentionally) exerting influence upon the context the system resides and is based on. By indirectly removing the building blocks of a system, it falls apart on its own. (Build something new, and the old fades away.)

Examples of the disregard approach would be the effects of inventing new technologies on industrial systems, or the effects of a massive shift of awareness on political systems.

Combining and varying these approaches is also possible.