Under your E-2 visa, you generally cannot take a part-time job with a different company. Your visa is tied exclusively to the specific enterprise that sponsored you, and working for any other employer is considered unauthorized employment. Engaging in such work is a serious violation of your immigration status and can lead to severe consequences, including the revocation of your visa, deportation, and being barred from re-entering the United States in the future.
For you to legally work a second job, the new employer would have to file a completely separate E-2 petition for you, a process known as "concurrent employment." You absolutely cannot begin this new job until U.S. Citizenship and Immigration Services (USCIS) has approved that new petition. Given the complexity of this process and the significant risks involved with any misstep, it is essential to consult with an experienced immigration attorney to discuss your options before proceeding.