This may be something you have to ask a CPA or tax attorney, but generally the answer will be yes. Some institutions will not allow you to open a self-employed 401(k) if you have more than one owner in the business, but by statutory definition these plans can be set up for partnerships.

If you are part of a partnership and this is where your self-employed income is made, you will be getting on thin ice if you attempt to form an LLC for yourself as a conduit for the money, just so you can have a self-employed 401(k), because, while that is not recommended, it will be about your best chance of setting up a Solo K that does not include your partners.

As far as the IRS is concerned, partners are part of a business, and cannot set up their own qualified plans. If Profit Sharing contributions are made to a Self-Employed 401(k) Plan, then they have to be made proportionally to the percentage of ownership for all business owners or shareholders of a Limited Liability Company (LLC).