Can my business that is registered to offer services (mostly B2B), also start selling physical products (mainly B2C)?

The short answer is yes, your business can operate in areas and types of business outside your company's stated business purpose. The longer answer is that this is generally known as the doctrine of ultra vires. An action by a corporation is considered ultra vires when it is outside the authority of the corporation. Thus, in jurisdictions that have adopted the ultra vires standard, any of these actions by a corporation are not binding, since a corporation cannot do more than it is authorized to do. Generally the ultra vires doctrine is a defense to an obligation owed by someone to a corporation.  However, Ohio explicitly excludes the ultra vires doctrine through R.C. 1701.13(H). This provision does not allow for any company to use the ultra vires, or outside of the stated business purpose, defense to void a contract or other obligation owed to your corporation.