Yes, if all four of you agree to the terms of the new one. However, most states that have authorized the formation of Limited Liability Companies in their states have also enacted default rules for these entities. In other words, even in the absence of an Operating Agreement, there are still ground rules created by your state legislature. Creating a new Operating Agreement may be unnecessary. However, if there are unique provisions that you desire to have incorporated into the Agreement (that are not addressed by state law) you can prepare and execute a new one.
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In CA, all members have to agree to amend an Operationg Agreement, so a new one would be like amending the old one.
An even number of members, if the membership shares are equal, could set you up for a tie, so one thing you might want to address in an LLC Operating Agreement is what happens in case of a tie and how that tie will be broken.
Also, it's not a good sign that not 1 of the 4 of you managed to hold on to the Operating Agreement - who is the tax matters partner? Where is the address of the LLC, and why isn't an original Operating Agreement there? Now is a good time to designate an LLC lawyer and/or CPA so this or something similar doesn't happen again.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Yes, you can sign a new operating agreement. In legalese, it would be referred to as the "Restated Operating Agreement of [LLC Name]" because it restates (replaces) the original.
The issue - which is very important for a multi-member LLC - then becomes how you will make sure that the OA has all of the appropriate provisions. I have included, below, a link to a variety of posts about LLC operating agreements. Perhaps you will find some of them helpful.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.