Can I split the payment of a purchase invoice across multiple treasuries?

Yes, you can do so directly when creating the purchase invoice.

• When creating a purchase invoice, enable the “Already Paid to the Supplier” option.
• From the Payment Method dropdown select “Multiple”.
• A table appears to add payment rows — add a row for each treasury or bank account and specify the payment method, treasury, and amount for each.
• Make sure the total of all amounts equals the invoice total before saving.

For more details refer to: Recording Multiple Payments When Creating a Purchase Invoice