Gene regulation is aided by epigenetics. Epigenetics determines which genes are turned off and which are switched on, and it varies throughout our lifetimes. Is it feasible that epigenetic modifications switch off the genes that determine whether a muscle cell or a neuron is a muscle cell or a neuron? I have searched this question but I could not find an explanation.
Correct me if I am wrong but it seems you are asking 'do epigenetic mechanisms influence cell fate/determination?'. If this is your question, the answer is yes. Epigenetic modifications play a key role in 'deciding' what type of cell a given stem cell will differentiate into. Here is some more information: https://www.nature.com/articles/pr2006122