Yes. It can be either on a full time or part time basis. A participant can be employed by an outside company. A person may even participate in an employer’s 401k plan in conjunction with their own solo 401k plan. However, they are still subject to rules governing maximum contributions.
Self-employment can take different forms. It would typically include ownership and operation of a sole proprietorship, Limited Liability Company (“LLC”), Corporation (including C Corps and S Corps) and a Limited Partnership where the business itself intends to generate profit (earned income).
Based on compensation and profits of the business, there are certain contribution limitations. Generally, you are considered eligible by the IRS if the business is being conducted with the intention of generating profits.