Can anyone share experiences with cloud-based file sharing solutions that are independent from in-company systems and meet the following requirements for a group of 10 companies with a total of 50 users? The solutions must support co-authoring of Microsoft documents, role-based permissions, multi-factor authentication (MFA), privacy and GDPR compliance, encryption at rest and in transit, and include ransomware scanning.

Box can do all of that, used them many times. Here is the link regarding Microsoft co-authoring https://support.box.com/hc/en-us/sections/21356589562131-Box-for-Microsoft-Office-Coauthoring

I only have significant experience with OneDrive and Google Drive, which doesn't really fit with what they are looking for.
I know of others like DropBox but haven't used them in a business environment.

Microsoft OneDrive for Business, Google Workspace (Google Drive) & Dropbox Business - All supports the requirement shared above. 

I see too many companies opting for third-party solutions whereas I think your requirements squarely point to Microsoft Azure with Office 365 which ticks all of the boxes. Microsoft owns login, and therefore MFA and RBP, as well as being the defacto standard, and therefore owns co-authoring. Vendor lock-in is just one element of cost and risk that has to be considered in a holistic evaluation of enterprise architecture. I understand some organisations have legacy investments in cisco and other solutions, or almost religious anti-Microsoft penchant or bias in their IT, but a shared tenant or federated tenants in Azure is going to be the cheapest, most secure, and most GDPR compliant option. Cisco Webex comes in a distant second, with a hefty dose of costly and risky integration and true GDPR compliance narrows it down to those two. 

#imho #ymmv

You may want to take a look at Box.Com 
We've used it for such cases with external partners.