Since you know that you owe taxes, your best option may be to file your return with appropriate payment before the April deadline. If you can, wait until you have the draft K-1 so you can estimate the income to be reported on the final K-1, which may reduce any interest on the tax you may owe later. But don't fail to file before the filing deadline.
When you receive the final Schedule K-1, you can amend your return and pay any additional tax.
Extending now will have no effect on the tax or interest you owe when you file later (or amend).
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