Official comment
These companies often advertise mutli currency handling, but without advising you of what is happening behind the scenes. They sometimes will link to a page like Stripe's Explanation, but you have to read that carefully to see what really happens to your customers.
They usually don't tell you about the drawbacks of this type of multi-currency handling. Stripe's page is worth a read .... your customer may have a surprise currency exchange fee on their bill of 1 - 3% of the total, PLUS foreign transaction fees (Stripe doesn't specify this but these are frequently 3 -- 5%).
Imagine clicking "Yes" on an order form to have it billed in your currency and then getting surprised when your credit card shows an extra 4 to 8% in fees on top of that. How often would you return to that vendor to buy stuff "In your currency!"?
Also not noted is that you can have currency exchange fees if you do not have a bank account in that foreign currency. The amount, in your customer's currency, is deposited into your regular bank account, and if your bank will accept it, they may automatically convert it to your home currency. And they may charge you an additional exchange fee.
What about those million dollar "Dynamic Currency Conversion" systems that are all the rage in the hotel industry? Read this travel blogger's warnings about it: The Points Guy on DCC.
The straight forward way to do this would be to use two ONTRAPORT accounts, each with a gateway for a specific currency, and each gateway attached to a bank account for that currency. Your customer gets billed in that currency, and it goes into a bank account in that currency. You are likely to still pay a conversion fee when you convert the foreign currency into your home currency.
There is one caveat though; your customer might still get a "foreign transaction fee" added if your company is not located in their country. US citizens buying from Australian business, for example, will usually pay an additional 1 - 3% even if they make the purchase in USD (there are a few credit cards that do not have a foreign transaction fee, so this will vary from customer to customer).
