Comment by proberts

The analysis is nuanced and the answer (which can be Yes or No) depends on a variety factors, such as what "running" the company involves, whether there are multiple founders, what the corporate structure of the company is, whether the company is generating revenues, whether the company has clients, whether the company has received funding, and whether the company has employees. To state the obvious, before embarking on such a venture, get a consultation so that you understand what's possible and what you can and can't do. There's also the option of getting a concurrent part-time H-1B to actually work for your startup.