Turning gene on is an example of what can happen in promotion event. The initiated cell will divide too. Some cells in an organ are removed or killed. This will make the remaining cells of that type divide faster than normal. Hormones often make cells divide.
Hormones also make certain genes turn on.
Immune system suppression can promote cancer. For example, people take drugs to suppress the immune system if they are getting an organ transplant or if they have an autoimmune disease. Immune stimulation, if chronic and excessive, can promote cancer. An example is when asbestos particles are in the lungs. The chemicals the macrophage uses to destroy invaders end up getting secreted continuously.