Yes, hormonal levels can be affected by a single hormone. For instance, hCG can increase the level of testosterone and progesterone as it is one of the reasons why hCG is used in many fertility treatments. in fact, it is also used in cases where young men tend to have delayed sexual development. Even Body builders who tend to have low testosterone levels use hcg to restore the testo levels after using steroid.
I do believe that all hormones work together and even a slightest tweak would influence the level of another. Having a balance is part of healthy life.