You are free to start a company while you are in F1 status, but as it’s already been mentioned, you can’t work for your own company (usually). In some instances, you may be able to prove that the work relates directly to your academics. In that case, you may be able to work for the company, but the position would definitely have to coincide with your degree goals.
Also, it may be possible to self-sponsor since UNCIS have updated their policies and it may be possible for individuals with an ownership stake in a company. However, the company has to be structured in a very specific way. For example, because you have to establish an employee-employer relationship, you will need to prove that the business has a board or committee that is control of hiring and firing employees. This is a bit of a complex situation so you would do best to consult a professional.
Other options may be available to you, but you should discuss that with an immigration attorney.can connect you with a highly skilled attorney that can outline your options and explain the requirements. Check out our webpage to learn more about what we do and to set up a consultation.