Yes it can, but it really isn’t a great idea. The chief drawback of operating as a sole proprietor is the fact that you remain personally liable for anything that goes wrong with your businesses. For example, if someone ever sued one of your businesses and an adverse judgment was rendered against it, then your personal assets, such as your home or car, would be susceptible to being used to satisfy any judgment award or lien. However, if your businesses are formally incorporated, then the assets of the corporation would be subject to any adverse judgment and you would typically avoid any personal liability.
Sole proprietorships work for very basic businesses which do not involve a great deal of risk. However, since you have multiple businesses, your situation seems to be fairly complex and so it would be worth your while to look into moving beyond a sole proprietorship and forming a more complex business entity such as a limited liability company (LLC). (take a look here for information on the benefits forming an LLC)
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