Vendor Invoice w/ different exchange rate on taxable amount and tax amount

Hi Experts,
I have an issue with regarding the Vendor Invoice with Foreign Currency. Normally we use JPY as our base currency and system exchange rate for out Vendor Invoices. But there was an audit issue pointing out that the Original Vendor Invoice is not tallied with the SAP Invoice as the tax amount is not the same. The problem is the Original Invoice has the Vendor Exchange Rate and it is not the same with the system rate that we use. Auditor tells us that we should use the Vendor Exchange Rate for Tax Amount and use the System Exchange Rate for the Taxable Amount. Is this possible? Can we use 2 Exchange Rates in a single Invoice Document one for the taxable amount and one for the tax amount? How can we possibly do this? Or any workaround?
Thanks a lot for the information!

I think its a bit misleading...The requirement is to post an Invoice with a base taxable amount of  Exchange Rate A and a tax amount of Exchange Rate B. The Base Currency is JPY and the System Currency is SGD. So the Report S_ALR_87012357 should see the amount in SGD there. The Issue is caused by the different exchange rate on the tax amount submitted by the Vendor Invoice.
Example: Vendor Invoice Amount: 926,413.00 JPY, then we created PO to Invoice with Base Currency JPYalso amounted 926,413.00 JPY. However, in the Vendor Invoice Amount, the Tax Chargeable is 923.00 SGD (based on their exchange rate 65.66 JPY per SGD). But our Exchange Rate (System Rate) is 63.49 JPY per SGD. How can we reflect the Tax Amount as 65.66 JPY but still the correct SGD amount is based on the Vendor Original Invoice Exchange Rate 65.66 and not the System Exchange Rate, 63.49 in the same Invoice Creation (MIRO)?

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