Hello Tim,
Without disagreeing with Bruce, that the organization itself can only have one year end, you can run the Year end function whenever you wish, and as many times throughout the year as you wish. You can also run year end by department, and close the P&L accounts to a Retrained Earning account specifically for that department.
You should work with your Adagio Consultant to determine the best way to make this work for you. Certainly you'll want financial statements tailored for that specific entity.
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Andrew Bates