I don't think there's such a hybrid all-in-one system because of the additional requirements and complications associated with receiving fiat. I think you would have to create your own system, possibly leveraging an existing Bitcoin payment system, combined with a fiat system, and integrate it into the same UX. I don't think you'd have any trouble using an existing bitcoin merchant solution alongside a seperate fiat system because there really wouldn't be any cross integrations between the two. You could use the UX as the front to direct users to either the bitcoin system, or the fiat system. That's my two sats.
What online payment gateway can collect payments in #Bitcoin...
But also has regular fiat payments, for those that don't have sats - those would be converted to BTC and arrive to merchant.
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Discussion
Thank you, that's what I thought. Are there any providers that receive fiat but send merchant Bitcoin?
Not sure, but it sounds like something Strike might do. It may require a two-step process in which they pay with fiat, and then you convert the fiat once a week to bitcoin.
You could also look at Coinos. They've got a merchant program for Bitcoin via on-chain and Lightning, and they also work with Shopify or something similar. Perhaps there's some solution to be had with their system.